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DO NOW. Take a blank notecard from the front bookshelf. Explain why the following statements are false. If you live in California, you live in Watts If the ground is wet, then it has been raining . Introduction to Logic. Logic and Reasoning. Today’s Objectives.

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Do now
DO NOW

  • Take a blank notecard from the front bookshelf.

  • Explain why the following statements are false.

    • If you live in California, you live in Watts

    • If the ground is wet, then it has been raining.


Introduction to logic

Introduction to Logic

Logic and Reasoning


Today s objectives
Today’s Objectives

  • Use counterexamples to disprove conditional statements.

  • Explain the relationship between hypothesis and conclusion.

  • Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement.

  • Use Problem Solving Skills


Conditional statement
Conditional Statement

  • An if-then statement

  • Symbolized by p –> q

  • Which p is a hypothesis and q is a conclusion.


Making a statement conditional
Making a statement conditional.

  • Get rid of the word “all” or “every.”

  • Replace it with “if”

  • Make sense of the statement (add necessary words)

    • Everyone who lives in Watts lives in California.

    • All trees are green.

    • Every teacher at Simon Tech is Canadian.


H ypothesis p
Hypothesis (p)

  • If you live in Watts, then you live in California.

  • If it has been raining, then the ground is wet.


Conclusion q
Conclusion (q)

  • If you live in Watts, then you live in California.

  • If it has been raining, then the ground is wet.


If hypothesis then conclusion
If hypothesis, then conclusion.

  • If p, then q.


C ounterexample
Counterexample

  • Proves that a conditional statement is false.

  • Fits the hypothesis but not the conclusion.


N egation
Negation

  • The statement the counterexample fits.

  • If p then not q.

  • If you live in Watts, then you do not live in California.


C onverse
Converse

  • Reversing the hypothesis and conclusion.

  • If q then p.

  • If you live in California, then you live in Watts.


I nverse
Inverse

  • Negating the hypothesis and conclusion.

  • If not p then not q.

  • If you do not live in Watts, then you do not live in California.


Contrapositive
Contrapositive

  • Negating the hypothesis and conclusion AND reversing them.

  • If not q then not p.

  • If you do not live in California, then you do not live in Watts.


Biconditional
Biconditional

  • The conditional and the converse combined

  • If p then q AND if q then p.

  • P if and only if q.

  • P iff q.

  • You live in California if and only if you live in Watts.


On your notecard
On your notecard…

  • Write a conditional statement. (in If-then form)



Today s objectives1
Today’s Objectives

  • Use counterexamples to disprove conditional statements.

  • Explain the relationship between hypothesis and conclusion.

  • Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement.

  • Use Problem Solving Skills


Exit slip
Exit slip

  • 1. Give a counterexample to the statement “If you are a student at Simon Tech, you live in Watts.”

  • 2. Explain the relationship between the hypothesis and conclusion. (You may use the statement in #1 or #3 if you would like.)

  • 3. If I receive a scholarship, I will go to college.

    • A. Write the negation.

    • B. Write the converse.

    • C. Write the inverse.

    • D. Write the contrapositive.

  • 4. Write a statement that you are a counterexample to.


Do now1
DO NOW

  • Take a blank notecard from the front bookshelf (for later).

  • In your notebook, explain why the following statements are false.

    • If you live in California, you live in Watts

    • If the ground is wet, then it has been raining.


Introduction to logic1

Introduction to Logic

Logic and Reasoning


Today s objectives2
Today’s Objectives

  • Use counterexamples to disprove conditional statements.

  • Explain the relationship between hypothesis and conclusion.

  • Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement.

  • Use Problem Solving Skills


Conditional statement1
Conditional Statement

  • An if-then statement

  • Symbolized by p –> q

  • Which p is a hypothesis and q is a conclusion.


Making a statement conditional1
Making a statement conditional.

  • Get rid of the word “all” or “every.”

  • Replace it with “if”

  • Make sense of the statement (add necessary words)

    • Everyone who lives in Watts lives in California.

    • All trees are green.

    • Every teacher at Simon Tech is Canadian.


H ypothesis p1
Hypothesis (p)

  • If you live in Watts, then you live in California.

  • If it has been raining, then the ground is wet.


Conclusion q1
Conclusion (q)

  • If you live in Watts, then you live in California.

  • If it has been raining, then the ground is wet.


If hypothesis then conclusion1
If hypothesis, then conclusion.

  • If p, then q.


C ounterexample1
Counterexample

  • Proves that a conditional statement is false.

  • Fits the hypothesis but not the conclusion.


N egation1
Negation

  • The statement the counterexample fits.

  • If p then not q.

  • If you live in Watts, then you do not live in California.


C onverse1
Converse

  • Reversing the hypothesis and conclusion.

  • If q then p.

  • If you live in California, then you live in Watts.


I nverse1
Inverse

  • Negating the hypothesis and conclusion.

  • If not p then not q.

  • If you do not live in Watts, then you do not live in California.


Contrapositive1
Contrapositive

  • Negating the hypothesis and conclusion AND reversing them.

  • If not q then not p.

  • If you do not live in California, then you do not live in Watts.


Biconditional1
Biconditional

  • The conditional and the converse combined

  • If p then q AND if q then p.

  • P if and only if q.

  • P iff q.

  • You live in California if and only if you live in Watts.


On your notecard1
On your notecard…

  • Write a conditional statement. (in If-then form)



Today s objectives3
Today’s Objectives

  • Use counterexamples to disprove conditional statements.

  • Explain the relationship between hypothesis and conclusion.

  • Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement.

  • Use Problem Solving Skills


Exit slip1
Exit slip

  • 1. Give a counterexample to the statement “If you are a student at Simon Tech, you live in Watts.”

  • 2. Explain the relationship between the hypothesis and conclusion. (You may use the statement in #1 or #3 if you would like.)

  • 3. If I receive a scholarship, I will go to college.

    • A. Write the negation.

    • B. Write the converse.

    • C. Write the inverse.

    • D. Write the contrapositive.

  • 4. Write a statement that you are a counterexample to.


Do now2
DO NOW

  • Take a blank notecard from the front bookshelf (for later).

  • In your notebook, explain why the following statements are false.

    • If you live in California, you live in Watts

    • If the ground is wet, then it has been raining.


Error analysis
Error Analysis

  • Compare your exit slip to this example.


Introduction to logic2

Introduction to Logic

Logic and Reasoning


Today s objectives4
Today’s Objectives

  • Use counterexamples to disprove conditional statements.

  • Explain the relationship between hypothesis and conclusion.

  • Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement.

  • Use Problem Solving Skills


Conditional statement2
Conditional Statement

  • An if-then statement

  • Symbolized by p –> q

  • Which p is a hypothesis and q is a conclusion.


Making a statement conditional2
Making a statement conditional.

  • Get rid of the word “all” or “every.”

  • Replace it with “if”

  • Make sense of the statement (add necessary words)

    • Everyone who lives in Watts lives in California.

    • All trees are green.

    • Every teacher at Simon Tech is Canadian.


H ypothesis p2
Hypothesis (p)

  • If you live in Watts, then you live in California.

  • If it has been raining, then the ground is wet.


Conclusion q2
Conclusion (q)

  • If you live in Watts, then you live in California.

  • If it has been raining, then the ground is wet.


If hypothesis then conclusion2
If hypothesis, then conclusion.

  • If p, then q.


C ounterexample2
Counterexample

  • Proves that a conditional statement is false.

  • Fits the hypothesis but not the conclusion.


N egation2
Negation

  • The statement the counterexample fits.

  • If p then not q.

  • If you live in Watts, then you do not live in California.


C onverse2
Converse

  • Reversing the hypothesis and conclusion.

  • If q then p.

  • If you live in California, then you live in Watts.


I nverse2
Inverse

  • Negating the hypothesis and conclusion.

  • If not p then not q.

  • If you do not live in Watts, then you do not live in California.


Contrapositive2
Contrapositive

  • Negating the hypothesis and conclusion AND reversing them.

  • If not q then not p.

  • If you do not live in California, then you do not live in Watts.


Biconditional2
Biconditional

  • The conditional and the converse combined

  • If p then q AND if q then p.

  • P if and only if q.

  • P iff q.

  • You live in California if and only if you live in Watts.


On your notecard2
On your notecard…

  • Write a conditional statement. (in If-then form)



Today s objectives5
Today’s Objectives

  • Use counterexamples to disprove conditional statements.

  • Explain the relationship between hypothesis and conclusion.

  • Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement.

  • Use Problem Solving Skills


Exit slip2
Exit slip

  • 1. Give a counterexample to the statement “If you are a student at Simon Tech, you live in Watts.”

  • 2. Explain the relationship between the hypothesis and conclusion. (You may use the statement in #1 or #3 if you would like.)

  • 3. If I receive a scholarship, I will go to college.

    • A. Write the negation.

    • B. Write the converse.

    • C. Write the inverse.

    • D. Write the contrapositive.

  • 4. Write a statement that you are a counterexample to.


Do now3
DO NOW

  • Take a blank notecard from the front bookshelf (for later).

  • In your notebook, explain why the following statements are false.

    • If you live in California, you live in Watts

    • If the ground is wet, then it has been raining.


Error analysis1
Error Analysis

  • Compare your exit slip to this example.


Introduction to logic3

Introduction to Logic

Logic and Reasoning


Today s objectives6
Today’s Objectives

  • Use counterexamples to disprove conditional statements.

  • Explain the relationship between hypothesis and conclusion.

  • Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement.

  • Use Problem Solving Skills


Conditional statement3
Conditional Statement

  • An if-then statement

  • Symbolized by p –> q

  • Which p is a hypothesis and q is a conclusion.


Making a statement conditional3
Making a statement conditional.

  • Get rid of the word “all” or “every.”

  • Replace it with “if”

  • Make sense of the statement (add necessary words)

    • Everyone who lives in Watts lives in California.

    • All trees are green.

    • Every teacher at Simon Tech is Canadian.


H ypothesis p3
Hypothesis (p)

  • If you live in Watts, then you live in California.

  • If it has been raining, then the ground is wet.


Conclusion q3
Conclusion (q)

  • If you live in Watts, then you live in California.

  • If it has been raining, then the ground is wet.


If hypothesis then conclusion3
If hypothesis, then conclusion.

  • If p, then q.


C ounterexample3
Counterexample

  • Proves that a conditional statement is false.

  • Fits the hypothesis but not the conclusion.


N egation3
Negation

  • The statement the counterexample fits.

  • If p then not q.

  • If you live in Watts, then you do not live in California.


C onverse3
Converse

  • Reversing the hypothesis and conclusion.

  • If q then p.

  • If you live in California, then you live in Watts.


I nverse3
Inverse

  • Negating the hypothesis and conclusion.

  • If not p then not q.

  • If you do not live in Watts, then you do not live in California.


Contrapositive3
Contrapositive

  • Negating the hypothesis and conclusion AND reversing them.

  • If not q then not p.

  • If you do not live in California, then you do not live in Watts.


Biconditional3
Biconditional

  • The conditional and the converse combined

  • If p then q AND if q then p.

  • P if and only if q.

  • P iff q.

  • You live in California if and only if you live in Watts.


On your notecard3
On your notecard…

  • Write a conditional statement. (in If-then form)



Today s objectives7
Today’s Objectives

  • Use counterexamples to disprove conditional statements.

  • Explain the relationship between hypothesis and conclusion.

  • Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement.

  • Use Problem Solving Skills


Exit slip3
Exit slip

  • 1. Give a counterexample to the statement “If you are a student at Simon Tech, you live in Watts.”

  • 2. Explain the relationship between the hypothesis and conclusion. (You may use the statement in #1 or #3 if you would like.)

  • 3. If I receive a scholarship, I will go to college.

    • A. Write the negation.

    • B. Write the converse.

    • C. Write the inverse.

    • D. Write the contrapositive.

  • 4. Write a statement that you are a counterexample to.


Do now4
DO NOW

  • Take a blank notecard from the front bookshelf (for later).

  • In your notebook, explain why the following statements are false.

    • If you live in California, you live in Watts

    • If the ground is wet, then it has been raining.


Error analysis2
Error Analysis

  • Compare your exit slip to this example.


Introduction to logic4

Introduction to Logic

Logic and Reasoning


Today s objectives8
Today’s Objectives

  • Use counterexamples to disprove conditional statements.

  • Explain the relationship between hypothesis and conclusion.

  • Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement.

  • Use Problem Solving Skills


Conditional statement4
Conditional Statement

  • An if-then statement

  • Symbolized by p –> q

  • Which p is a hypothesis and q is a conclusion.


Making a statement conditional4
Making a statement conditional.

  • Get rid of the word “all” or “every.”

  • Replace it with “if”

  • Make sense of the statement (add necessary words)

    • Everyone who lives in Watts lives in California.

    • All trees are green.

    • Every teacher at Simon Tech is Canadian.


H ypothesis p4
Hypothesis (p)

  • If you live in Watts, then you live in California.

  • If it has been raining, then the ground is wet.


Conclusion q4
Conclusion (q)

  • If you live in Watts, then you live in California.

  • If it has been raining, then the ground is wet.


If hypothesis then conclusion4
If hypothesis, then conclusion.

  • If p, then q.


C ounterexample4
Counterexample

  • Proves that a conditional statement is false.

  • Fits the hypothesis but not the conclusion.


N egation4
Negation

  • The statement the counterexample fits.

  • If p then not q.

  • If you live in Watts, then you do not live in California.


C onverse4
Converse

  • Reversing the hypothesis and conclusion.

  • If q then p.

  • If you live in California, then you live in Watts.


I nverse4
Inverse

  • Negating the hypothesis and conclusion.

  • If not p then not q.

  • If you do not live in Watts, then you do not live in California.


Contrapositive4
Contrapositive

  • Negating the hypothesis and conclusion AND reversing them.

  • If not q then not p.

  • If you do not live in California, then you do not live in Watts.


Biconditional4
Biconditional

  • The conditional and the converse combined

  • If p then q AND if q then p.

  • P if and only if q.

  • P iff q.

  • You live in California if and only if you live in Watts.


On your notecard4
On your notecard…

  • Write a conditional statement. (in If-then form)



Today s objectives9
Today’s Objectives

  • Use counterexamples to disprove conditional statements.

  • Explain the relationship between hypothesis and conclusion.

  • Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement.

  • Use Problem Solving Skills


Exit slip4
Exit slip

  • 1. Give a counterexample to the statement “If you are a student at Simon Tech, you live in Watts.”

  • 2. Explain the relationship between the hypothesis and conclusion. (You may use the statement in #1 or #3 if you would like.)

  • 3. If I receive a scholarship, I will go to college.

    • A. Write the negation.

    • B. Write the converse.

    • C. Write the inverse.

    • D. Write the contrapositive.

  • 4. Write a statement that you are a counterexample to.


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