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.
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 " .
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