Conditional Statements. Quiz The 'jQuery Template' JavaScript: Conditional Statements 2.
2-3 Conditional Statements- Related What are the three related conditional statements? How are the...
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Transcript of 2-3 Conditional Statements- Related What are the three related conditional statements? How are the...
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2-3 Conditional Statements- Related
What are the three related conditional
statements?
How are the three related conditional statements made?
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• Analyze statements in if-then form.
• Write the converse, inverse, and contrapositive of if-then statements.
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Related StatementsThere are related conditionals that are based
on a given conditional statement. They are:
Converse
Inverse
Contrapositive
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ConverseThe converse of a conditional statement is
formed by exchanging the hypothesis and the conclusion.
(Converse—con—switch)
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Converse (Switch if-then)
Conditional:
If you live in Mishawaka, then you live in Indiana.
Converse:
If you live in Indiana, then you live in Mishawaka.
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Inverse
The inverse of a conditional is formed by negating both the hypothesis and the conclusion.
(Negations state the opposite of the original phrase.)
Add not or take not out
not
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Inverse (add not)
Conditional:
If you live in Mishawaka, then you live in Indiana.
Inverse:
If you don’t live in Mishawaka, then you don’t live in Indiana.
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Contrapositive The contrapositive of a conditional is formed by
negating the hypothesis and conclusion, then interchanging them.
Switch and add not.
+not
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Contrapositive(switch & add not)
Conditional:
If you live in Mishawaka, then you live in Indiana.
Contrapositive:
If you don’t live in Indiana, then you don’t live in Mishawaka.
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If you are a teenager, then you are 15.
Converse:
If you are 15, then you are a teenager.
Inverse:
If you are not a teenager, then you are not 15.
Contrapositive:
If you are not 15, then you are not a teenager.
true
true
false
false
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In your book on page 109
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Statements with the same truth value are said to be logically equivalent.
A conditional and its contrapositive are either both true or both false. Similarly, the converse and inverse of a conditional are either both true or both false.
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If you water the plants, then the plants will grow.
Converse:
If the plants grow, then you watered the plants.
Inverse:
If you don’t water the plants, then the plants will not grow.
Contrapositive:
If the plants do not grow, then you did not water the plants.
true
true
true
true
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NATURE Write the converse, inverse, and contrapositive of the following true statement. Determine the truth value of each statement. If a statement is false, give a counterexample.
.
Bats are not birds, they are mammals.Bats have modified
hands and armsthat serve as wings.They are the only
mammals that can fly.
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Conditional: First, rewrite the conditional in if-then form.
If an animal is a bat, then it can fly.
Bats are animals that can fly
Converse: If an animal can fly, then it is a bat.
Counterexample: A bird is an animal that can fly, but it is not a bat.
Inverse: If an animal is not a bat, then it cannot fly.
Counterexample: A bird is not a bat, but it is an animal that can fly.
Contrapositive: If an animal cannot fly, then it is not a bat.
T
F
F
T
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Check Check to see that logically equivalent statements have the same truth value.
Both the conditional and contrapositive are true.
Both the converse and inverse are false.
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2-3 Assignment day 2
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