PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true...
Transcript of PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true...
+ 2.2: Analyze Conditional Statements
+Conditional Statement Has two parts…
*Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To be false, only one counterexample is needed
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1. If an angle is 90 degrees, then it is a right angle
2. If x = -3, then 2x + 7 = 1
3. If n = 9, then n squared is 81
4. If tourists are at the Alamo, then they are in in TX
+Negation: Opposite of the original statement
+Related Conditionals
Conditional Statement: Hypothesis and Conclusion
Inverse: Negate Conditional Statement
Converse: Exchange Hypothesis and Conclusion
Contrapositive: negate the Converse
**Equivalent Statements
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Conditional Statement: Hypothesis and Conclusion
Inverse: negate Conditional Statement
Converse: Exchange Hypothesis and Conclusion
Contrapositive: negate the Converse
If you are a guitar player, then you are a musician
If you are a musician, then you are a guitar player
If you are NOT a guitar player, then you are NOT a musician
If you are NOT a musician, then you are NOT a guitar player
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Conditional Statement: Hypothesis and Conclusion
Inverse: negate Conditional Statement
Converse: Exchange Hypothesis and Conclusion
Contrapositive: negate the Converse
If a dog is a Great Dane, then it is large
If a dog is large, then it is a Great Dane
If a dog is NOT a Great Dane, then it is NOT a dog
If a dog is NOT large, it is NOT a Great Dane
On your own: Related Conditionals
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Conditional Statement: Hypothesis and Conclusion
Inverse: negate Conditional Statement
Converse: Exchange Hypothesis and Conclusion
Contrapositive: negate the Converse
If a polygon is equilateral, then the polygon is regular
If a polygon is regular, then the polygon is equilateral
If a polygon is NOT equilateral, then it is NOT regular
If a polygon is NOT regular, then the polygon is NOT equilateral
On your own: Related Conditionals
+Definitions of words Can be written as conditional statements (if-then) and or as its converse. Both are true
+Biconditional Statement Any true definition can use the phrase “if and only if” in a statement because both the conditional statement and its converse are true.
+ Rewrite the statement as biconditional “If Mary is in theater class, she will be in the fall play. If Mary is in the fall play, she must be taking theater class”
Biconditional: “Mary is in the theater class IF AND ONLY IF she will be in the fall play.”
“Mary will be in the fall play IF AND ONLY IF she is in theater class.”
OR
+ Decide Whether Each Statement about the Diagram is True or False
TRUE!
FALSE!
TRUE!
+ Decide whether each statement is true or false
SO TRUE!
SO TRUE!
SO FALSE!
SO FALSE!
+Homework: p. 82 (1-29)