Given, the logical statement is: The necessary and sufficient condition for raining is that there should

be clouds in the sky.

Let P denotes raining, and Q denotes there should be clouds in the sky.

So, the given statement can write it in mathematically as: 

     P ⇔ Q

or (P → Q) ∧ (Q → P)

or (~P ∨ Q) ∧ (~Q ∨ P)