Incorrect Negation, Incorrect Reversal, and the Contrapositive

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6 Terms

1
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An Incorrect negation (IN) is when you

take a conditional statement and simply negate both the sufficient and necessary conditions.

2
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An Incorrect reversal (IR) is when you

Swap the sufficient and necessary conditions in a conditional statement

3
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A contrapositive (valid) is when you

Swap the sufficient and necessary condition in a conditional statement AND you negate both of them.

4
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Example of Incorrect Reversal

If I am in Los Angeles then I am in California (LA→CA)

If I am in California then I am in Los Angeles

(CA→LA)

THIS IS AN IR OF THE TOP STATEMENT. This does not work because you can be in California but not necessarily in LA.

5
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Example of Incorrect Negation

If I am in Los Angeles then I am in California (LA→CA)

If I am not in Los Angeles then I am not in California

(~LA → ~CA)

THIS IS AN IN OF THE TOP STATEMENT. It does not work because you could be in a city that is not LA and still be in California

6
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Contrapositive example

If I am in Los Angeles then I am in California (LA→CA)

If I am not in California then I am not in Los Angeles

(~CA → ~LA )

THIS IS A CONTRAPOSITIVE OF THE FIRST STATEMENT. This works because if you are not in California, there is no way you can be in Los Angeles. This worked because instead of just negating or just swapping the sufficient and necessary conditions, we did BOTH.