sLet $T=\{17\}, U=\{6\}, V=\{24\}$ and $W=\{2,3,7,26\}$. In which of these four different universes is the statement true?
a) $(\exists x)(x\,odd\implies x>8)$
b) $(\exists x)(x\, odd\wedge x>8)$
c) $(\forall x)(x\,odd\implies x>8)$
d) $(\forall x)(x\, odd\wedge x>8)$
For a) I said $T, U, V$ and $W$. (because we can even choose an $x$ which isn't odd and the implication will be true)
For b) I said $T$. (This is because it should have both conditions, unlike with implication)
For c) I said $T, U, V$. (There is 7 which doesn't satisfy the implication in $W$, so the rest is true because forall and exists have the same meaning if the set have only one element)
For d) I said $T$ (both conditions again, for all elements, that's why)
Is this true ?
Your answers and argumentation are spot-on. There's nothing more to add really. Cheers!