Proposition into spoken language

Question

Given:

$\sim( p \leftrightarrow (q \vee r) )$

$p:$ It's raining

$q:$ The sun is shining

$r:$ There are clouds in the sky.

Translate the proposition into spoken language.

Solution:

It's false that it's raining if and only if the sun is shining or there are clouds in the sky.

Would the solution above be okay?

Answer 1

$\sim(A\leftrightarrow B)\equiv (A\leftrightarrow \sim B)$.

So $\sim(p\leftrightarrow(q\vee r)\equiv p\leftrightarrow (\sim q \wedge \sim r)$

So I'd suggest: It's raining if and only if the sun is not shining and there are no clouds in the sky.

[I wonder if your $r$ should be 'there are no clouds in the sky'. That would make more sense.]

Answer 2

Your translation is perfectly adequate. Another suggestion:

It's not the case that it's raining if and only if the sun is shining or there are clouds in the sky.