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.

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

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

  • $\begingroup$ That's it!! Thank you so much!!! $\endgroup$ – Hani Gotc Dec 11 '13 at 11:41

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