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The contrapositive of p → q is the proposition of ____

Question

The contrapositive of p → q is the proposition of ____

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Solution

The contrapositive of p → q is the proposition of ¬q → ¬p.

Here's the step by step explanation:

  1. The original statement is p → q, which can be read as "if p then q".

  2. The contrapositive of a statement is formed by negating both the hypothesis and the conclusion, and then reversing the direction of the implication.

  3. So, for the statement p → q, the contrapositive would be "if not q then not p", which is symbolically represented as ¬q → ¬p.

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Similar Questions

The contrapositive of p → q is the proposition of ____________ans.q → p¬p → ¬q ¬q → p¬q → ¬p

Which of the following the logic representation of proof by contrapositive?Question 1Select one:a.P → Q = ¬Q → ¬Pb.P → Q = ¬Q → Pc.P → Q = Q → ¬Pd.P → Q = ¬(Q → P)

p → q is logically equivalent to ________

A proof that p → q is true based on the fact that q is true, such proofs are known as ___________ a. Direct proof b. Contrapositive proofs c. Trivial proof d. Proof by cases

p → q is logically equivalent to ________ ans. ¬p ∨ q ¬p ∨ ¬q p ∨ ¬q ¬p ∧ q

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