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Warm Up March 12, 2014. B. D , E, and F are midpoints. 8. 10. What is th e length of AB What is length of CD. E. D. 4. G. 8. C. A. F. EOCT Week 9 #3. Conditional Statements. Also known as logic statements. Types: Conditional, Inverse, Converse, & Contrapositive.

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Warm up march 12 2014

Warm Up March 12, 2014

B

D, E, and F are midpoints.

8

10

What is the length of AB

What is length of CD

E

D

4

G

8

C

A

F



Conditional statements

Conditional Statements

Also known as logic statements.

Types: Conditional, Inverse, Converse, & Contrapositive


A conditional statements
a. Conditional Statements

  • Called if-then statements

  • Have 2 parts

  • Hypothesis- The part afterif.

  • Conclusion- The part afterthen.

    * Do not include if and then in the hypothesis and conclusion.


Hypothesis and conclusion
Hypothesis and Conclusion

  • Example:

    If you are not satisfied for any reason, then return everything within 14 days for a full refund.


Examples identify the hypothesis and the conclusion
Examples: Identify the Hypothesis and the conclusion.

  • it is Saturday

  • Beckham plays soccer

  • points are collinear

  • they lie on the same line

1. If it is Saturday, then Beckham plays soccer.

  • Hypothesis-

  • Conclusion-

    2. If points are collinear, then they lie on the same line.

  • Hypothesis-

  • Conclusion-


Negation
Negation

A statement can be altered by negation by writing the negative of the statement

Symbol: ~


B inverse
b. Inverse

When you negate the hypothesis and conclusion of a conditional statement, you form the inverse.


Inverse
Inverse

  • The inverse of a conditional statement is formed by negatingboth the hypothesis and the conclusion in the conditional

    (Add “NOT”)

    Conditional- If a figure is a triangle, then it has three angles.

    • Inverse- If a figure is not a triangle, then it does not have three angles.


C converse
c. Converse

  • The converse of a conditional statement swaps the hypothesis and the conclusion.

    • Conditional- If a figure is a triangle, then it has three angles.

    • Converse- If a figure has three angles, then it is a triangle.


Converses are not always true
* Converses are not always true.

  • Conditional- If a figure is a square, then it has four sides.

  • Converse- If a figure has four sides, then it is a square.

    * Not all four sided figures are squares. Rectangles also have four sides.


Counterexample
Counterexample

Giving at least 1 example that disproves the statement.

  • Example: All prime numbers are odd.


Contrapositive
Contrapositive

  • The contrapositive of a conditional statement is formed by switching and negatingboth the hypothesis and the conclusion.

    (SWITCH the order and NEGATE)

    • Conditional- If a figure is a triangle, then it has three angles.

    • Contrapositive- If it does not have three angles, then a figure is not a triangle.


Recap
Recap

Conditional: p → q

Inverse: ~p → ~ q

Converse: q → p

Contrapositive: ~ q → ~ p


Truth value
Truth Value

Decide whether the statement is true or false. If false, give a counterexample as to why it’s false.

STMT: If you are a basketball player, then you are an athlete.

Converse:

Inverse:

Contrapositive:

False, not all athletes play basketball. Could play baseball, golf, tennis, swim, etc.

False, even if you don’t play basketball, you can still be an athlete. Again, could play baseball, golf, tennis, swim, etc.

True



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