There is a pack of cards and every card has a number on one side and a letter on the other. The statement that every card in this pack that has an A on one side has a 3 on the other side is true. The following cards are on the table:
A 3 7 D
Which card or cards would you turn if you are looking for an example that makes the statement above false? Why?
On
The statement you consider is $$\forall x,~(A(x) \to 3(x)),$$ where $A(x)$ means "There is a $A$ on one side of the card" and $3(x)$ means "there is a three on one side of the card".
Its negation is thus $$\exists x,~A(x)\land \lnot 3(x).$$
So, you want a card which both have an $A$ and not a $3$. The only cards possibly satisfying that are the one with $A$ (the one with $D$ cannot have an $A$), and the one with $7$ (the one with $3$, well, has a $3$).
My first choice would be the card facing "$A$", which yields a probability of $\frac{9}{10}$ for refuting the statement (if we assume $10$ possible numbers).
My second choice would the card facing "$7$", which yields a probability of $\frac{1}{26}$ for refuting the statement (if we assume $26$ possible letters).
The cards facing "$3$" and "$D$" could not be used in order to refute the statement.