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Question
The contrapositive of the statement “If 7 is greater than 5, then 8 is greater than 6” is ______.
Options
If 8 is greater than 6, then 7 is greater than 5
If 8 is not greater than 6, then 7 is greater than 5
If 8 is not greater than 6, then 7 is not greater than 5
If 8 is greater than 6, then 7 is not greater than 5
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Solution
The contrapositive of the statement “If 7 is greater than 5, then 8 is greater than 6” is if 8 is not greater than 6, then 7 is not greater than 5.
Explanation:
Let p: 7 is greater than 5
q: 8 is greater than 6
∴ p → q i.e., ~ p: 7 is not greater than 5.
And ~ q: 8 is not greater than 6.
So ~ p → ~ q: If 8 is not greater than 6, then 7 is not greater than 5.
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