The contrapositive of p → q is the proposition of ____________ans.¬q → p¬p → ¬q ¬q → ¬pq → p Previous Marked for Review Next
Question
The contrapositive of p → q is the proposition of ____________ans.
¬q → p¬p → ¬q¬q → ¬pp → ¬q
Solution
The contrapositive of p → q is ¬q → ¬p. This is a fundamental concept in logic and mathematics. Here's how it works:
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Start with the original statement, p → q. This can be read as "if p then q."
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The contrapositive of a statement is formed by negating both the hypothesis and the conclusion, and then reversing the direction of the implication.
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So, for p → q, we first negate p and q to get ¬p and ¬q.
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Then we reverse the direction of the implication to get ¬q → ¬p.
So, the contrapositive of p → q is ¬q → ¬p.
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