# The contrapositive of the statement " If it is raining, I will not come." is

A. If I will come then it is not raining.

B. If I will not come then it is raining.

C. If I will come then it is raining.

D. If I will not come then it is not raining.

Last updated date: 19th Mar 2023

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Answer

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Hint: Contrapositive means switching the hypothesis and conclusion of a conditional statement and negating both. The contrapositive of a conditional statement of the form "If p then q" is "If $ \sim q$ then $ \sim p$ ". Symbolically, the contrapositive of p q is $ \sim q \sim p$ .

Complete step-by-step answer:

Let us divide the statement into two parts P and Q .

P - If it is raining

Q - I will not come

i.e. P conditional to Q

We know that the contrapositive of $a \to b$ is $ \sim b \to \sim a$

Therefore the contrapositive of the statement becomes

If I come then it is not raining.

Note: Always remember that the contrapositive of a proposition or theorem formed by contradicting both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem and interchanging them "if not-B then not-A " is the contrapositive of "if A then B " .

Complete step-by-step answer:

Let us divide the statement into two parts P and Q .

P - If it is raining

Q - I will not come

i.e. P conditional to Q

We know that the contrapositive of $a \to b$ is $ \sim b \to \sim a$

Therefore the contrapositive of the statement becomes

If I come then it is not raining.

Note: Always remember that the contrapositive of a proposition or theorem formed by contradicting both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem and interchanging them "if not-B then not-A " is the contrapositive of "if A then B " .

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