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

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.

• Here you are defining $A=R$ and $B=R$. That is probably not your intention. – drhab Dec 11 '13 at 11:24
• I am? not of course not it's not my intention. should remove this relation R? – Hani Gotc Dec 11 '13 at 11:25
• you are saying: $A=\left\{ x\mid x\in R\right\}$ wich means exactly the same as $A=R$ – drhab Dec 11 '13 at 11:26
• sheesh That's not what I want – Hani Gotc Dec 11 '13 at 11:27
• Should remove this Relation? Do you think it is complicating more than it is helping? Do u understand what i meanr? – Hani Gotc Dec 11 '13 at 11:29

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