2-3 c onditionals. s tatements conditional statement a statement that can be written in if-then form...

2-3 CONDITIONALS

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2-3 CONDITIONALS

STATEMENTS

Conditional statement A statement that can be written in if-then form

If-Then statement If p, then q

“p” and “q” are statements “p” is the hypothesis “q” is the conclusion

EXAMPLE Identify the hypothesis and conclusion of the following statement.

Answer: Hypothesis: A polygon has 6 sides.Conclusion: It is a hexagon.

If a polygon has 6 sides, then it is a hexagon.

hypothesis conclusion

Page 4: 2-3 C ONDITIONALS. S TATEMENTS Conditional statement A statement that can be written in if-then form If-Then statement If p, then q “p” and “q” are statements

EXAMPLE

A. Hypothesis: You will cry.Conclusion: You are a baby.

B. Hypothesis: You are a baby.Conclusion: You will cry.

C. Hypothesis: Babies cry.Conclusion: You are a baby.

D. none of the above

Which of the choices correctly identifies the hypothesis and conclusion of the given conditional?

If you are a baby, then you will cry.

Page 5: 2-3 C ONDITIONALS. S TATEMENTS Conditional statement A statement that can be written in if-then form If-Then statement If p, then q “p” and “q” are statements

EXAMPLE Write a Conditional in If-Then Form

Write the statement in if-then form. Then identify the hypothesis and conclusion of the statement.

A five-sided polygon is a pentagon.

Answer: If a polygon has five sides, then it is a pentagon.

Hypothesis: A polygon has five sides.Conclusion: It is a pentagon.

Page 6: 2-3 C ONDITIONALS. S TATEMENTS Conditional statement A statement that can be written in if-then form If-Then statement If p, then q “p” and “q” are statements

EXAMPLE

A. If an angle is acute, then it measures less than 90°.

B. If an angle is not obtuse, then it is acute.

C. If an angle measures 45°, then it is an acute angle.

D. If an angle is acute, then it measures 45°.

Which of the following is the correct if-then form of the given statement?

An angle that measures 45° is an acute angle.

Page 7: 2-3 C ONDITIONALS. S TATEMENTS Conditional statement A statement that can be written in if-then form If-Then statement If p, then q “p” and “q” are statements

EXAMPLE Truth Values of Conditionals

Determine the truth value of the conditional statement. If true, explain your reasoning. If false, give a counterexample.

If last month was February, then this month is March.

True; March is the month that follows February.

Page 8: 2-3 C ONDITIONALS. S TATEMENTS Conditional statement A statement that can be written in if-then form If-Then statement If p, then q “p” and “q” are statements

EXAMPLE Determine the truth value of the conditional statement. If true, explain your reasoning. If false, give a counterexample.

The product of whole numbers is greater than or equal to 0.

A. True; 3 ● 5 = 15, 8 ● 2 = 16

B. False; –3 ● 4 = –12

Page 9: 2-3 C ONDITIONALS. S TATEMENTS Conditional statement A statement that can be written in if-then form If-Then statement If p, then q “p” and “q” are statements

CONVERSE

Switch the “if” and “then” Think opposite, or CON-artist

If q, then p.

Example:If today is Friday, then tomorrow is Saturday

TrueConverse

If tomorrow is Saturday, then today is FridayTrue

Underline hypothesis once

Underline conclusion twice

Page 10: 2-3 C ONDITIONALS. S TATEMENTS Conditional statement A statement that can be written in if-then form If-Then statement If p, then q “p” and “q” are statements

TOO

Think of your own “if-then” statement where the original statement is true, but the converse is false

Anyone want to share???

Page 11: 2-3 C ONDITIONALS. S TATEMENTS Conditional statement A statement that can be written in if-then form If-Then statement If p, then q “p” and “q” are statements

P: HYPOTHESIS Q: CONCLUSION

Recall: Statement If p, then q

Recall: Converse If q, then p (con-artist—does a switch)

Inverse If not p, then not q Add a word In---not

Contrapositive If not q, then not p Weirdest word—so do both, add NOT and Switch

Page 12: 2-3 C ONDITIONALS. S TATEMENTS Conditional statement A statement that can be written in if-then form If-Then statement If p, then q “p” and “q” are statements

EXAMPLES: Give the Converse, Inverse and Contrapos. State Tor F

If a parallelogram is a square, then it is a rectangle. (T) C: If a parallelogram is a rectangle, then it is a square. (F)

I: If a parallelogram is not a square, then it is not a rectangle (F)

C+: If a parallelogram is not a rectangle, then it is not a square (T)

Page 13: 2-3 C ONDITIONALS. S TATEMENTS Conditional statement A statement that can be written in if-then form If-Then statement If p, then q “p” and “q” are statements

RULE!!!!!!!!!!!!!!

Related conditionals A conditional statement and its contrapositive are logically equivalent. Either both are true or both are false.

- The converse and the inverse are logically equivalent. Either both are true or both are false.

Page 14: 2-3 C ONDITIONALS. S TATEMENTS Conditional statement A statement that can be written in if-then form If-Then statement If p, then q “p” and “q” are statements

HOMEWORK! (WRITE IT DOWN!!!!!!!!)

Pg.111 #19-51 odd(skip #41) 53-56, 58-61, 68 ALL

ON a Separate paper!!!!!!!!!!!

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