Formulate a relation $R$ between $2$ sets $A$ and $B$

Question

Let $A$ and $B$ be $2$ sets of real numbers. How can I formulate the following entence, in mathematical terms, not plain english.

IF At least one Element $x$ of $A$ is equal to one element $y$ of $B$ then It's raining else sunny.

Answer 1

$\left[\exists x\in A\exists y\in B\; x=y\Rightarrow\text{it is sunny}\right]\wedge\left[\forall x\in A\forall y\in B\; x\neq y\Rightarrow\text{it is rainy}\right]$