2-3 c onditionals. s tatements conditional statement a statement that can be written in if-then form...
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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.
If a polygon has 6 sides, then it is a hexagon.
hypothesis conclusion
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.
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.
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.
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.
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
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
TOO
Think of your own “if-then” statement where the original statement is true, but the converse is false
Anyone want to share???
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
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)
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.
HOMEWORK! (WRITE IT DOWN!!!!!!!!)
Pg.111 #19-51 odd(skip #41) 53-56, 58-61, 68 ALL
ON a Separate paper!!!!!!!!!!!