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

We begin by recalling the fundamental logical rule about contrapositives. For any implication of the form $$P \Rightarrow Q$$, the contrapositive is obtained by simultaneously negating both the hypothesis and the conclusion and reversing their order. In symbols, the contrapositive of $$P \Rightarrow Q$$ is $$\neg Q \Rightarrow \neg P$$, where $$\neg$$ stands for “not.” This rule is routinely taught in elementary logic and is guaranteed to give a statement that is logically equivalent to the original implication.

In the given English sentence, the parts can be identified as follows:

• Hypothesis $$P$$ : “It is raining.”

• Conclusion $$Q$$ : “I will not come.”

Translating the original sentence into symbolic form, we have

$$P \Rightarrow Q$$

which reads “If it is raining, then I will not come.”

Now we apply the rule for the contrapositive. First we negate the conclusion $$Q$$. The conclusion “I will not come” is negated to become “I will come.” Symbolically, $$\neg Q$$ means “I will come.”

Next we negate the hypothesis $$P$$. The hypothesis “It is raining” is negated to become “It is not raining.” Symbolically, $$\neg P$$ means “It is not raining.”

Finally, we reverse the order, writing $$\neg Q$$ first and $$\neg P$$ second, and we retain the implication arrow $$\Rightarrow$$ between them. Thus the contrapositive is expressed symbolically as

$$\neg Q \Rightarrow \neg P$$

which translates back into English as

“If I will come, then it is not raining.”

Comparing this English sentence with the four options provided, we see that it matches exactly with Option A:

Option A. if I will come, then it is not raining.

Hence, the correct answer is Option A.