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### Introduction to Logic

### Introduction to Logic

Today’s Objectives

### Introduction to Logic

Today’s Objectives

Today’s Objectives

### Introduction to Logic

Today’s Objectives

Conditional Statement

Making a statement conditional.

Hypothesis (p)

Conclusion (q)

Counterexample

Negation

Converse

Inverse

Contrapositive

Biconditional

Today’s Objectives

Exit slip

DO NOW

### Introduction to Logic

Today’s Objectives

Conditional Statement

Making a statement conditional.

Hypothesis (p)

Conclusion (q)

Counterexample

Negation

Converse

Inverse

Contrapositive

Biconditional

Today’s Objectives

Exit slip

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.

Logic and Reasoning

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

- An if-then statement
- Symbolized by p –> q
- Which p is a hypothesis and q is a conclusion.

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.

Hypothesis (p)

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

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

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 p, then q.

Counterexample

- Proves that a conditional statement is false.
- Fits the hypothesis but not the conclusion.

Negation

- The statement the counterexample fits.
- If p then not q.
- If you live in Watts, then you do not live in California.

Converse

- Reversing the hypothesis and conclusion.
- If q then p.
- If you live in California, then you live in Watts.

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

- 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

- 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…

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

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

- 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 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.

Logic and Reasoning

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

- An if-then statement
- Symbolized by p –> q
- Which p is a hypothesis and q is a conclusion.

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.

Hypothesis (p)

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

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

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 p, then q.

Counterexample

- Proves that a conditional statement is false.
- Fits the hypothesis but not the conclusion.

Negation

- The statement the counterexample fits.
- If p then not q.
- If you live in Watts, then you do not live in California.

Converse

- Reversing the hypothesis and conclusion.
- If q then p.
- If you live in California, then you live in Watts.

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

- 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

- 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…

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

- Use counterexamples to disprove conditional statements.
- Explain the relationship between hypothesis and conclusion.
- Use Problem Solving Skills

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 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

- Compare your exit slip to this example.

Logic and Reasoning

- Use counterexamples to disprove conditional statements.
- Explain the relationship between hypothesis and conclusion.
- Use Problem Solving Skills

Conditional Statement

- An if-then statement
- Symbolized by p –> q
- Which p is a hypothesis and q is a conclusion.

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.

Hypothesis (p)

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

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

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 p, then q.

Counterexample

- Proves that a conditional statement is false.
- Fits the hypothesis but not the conclusion.

Negation

- The statement the counterexample fits.
- If p then not q.
- If you live in Watts, then you do not live in California.

Converse

- Reversing the hypothesis and conclusion.
- If q then p.
- If you live in California, then you live in Watts.

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

- 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

- 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…

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

- Use counterexamples to disprove conditional statements.
- Explain the relationship between hypothesis and conclusion.
- Use Problem Solving Skills

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 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

- Compare your exit slip to this example.

Logic and Reasoning

- Use counterexamples to disprove conditional statements.
- Explain the relationship between hypothesis and conclusion.
- Use Problem Solving Skills

- An if-then statement
- Symbolized by p –> q
- Which p is a hypothesis and q is a conclusion.

- 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.

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

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

- 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 p, then q.

- Proves that a conditional statement is false.
- Fits the hypothesis but not the conclusion.

- The statement the counterexample fits.
- If p then not q.
- If you live in Watts, then you do not live in California.

- Reversing the hypothesis and conclusion.
- If q then p.
- If you live in California, then you live in Watts.

- 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.

- 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.

- 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…

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

- Use counterexamples to disprove conditional statements.
- Explain the relationship between hypothesis and conclusion.
- Use Problem Solving Skills

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

- 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

- Compare your exit slip to this example.

Logic and Reasoning

- Use counterexamples to disprove conditional statements.
- Explain the relationship between hypothesis and conclusion.
- Use Problem Solving Skills

- An if-then statement
- Symbolized by p –> q
- Which p is a hypothesis and q is a conclusion.

- 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.

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

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

- 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 p, then q.

- Proves that a conditional statement is false.
- Fits the hypothesis but not the conclusion.

- The statement the counterexample fits.
- If p then not q.
- If you live in Watts, then you do not live in California.

- Reversing the hypothesis and conclusion.
- If q then p.
- If you live in California, then you live in Watts.

- 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.

- 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.

- 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…

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

- Use counterexamples to disprove conditional statements.
- Explain the relationship between hypothesis and conclusion.
- Use Problem Solving Skills

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