Let $F(x)$ be the predicate “x is a frog”, $T(x)$ be “x has a long tongue”, and $J(x)$ be the predicate “x likes to jump”. The universe of discourse is all animals.
I'm asked to write: Every frog has a long tongue and likes to jump.
I came up with two answers and I am struggling to figure out which one of them would be the correct one (assuming that any of them are correct). I was wondering if someone could distinguish the difference between the two.
$\forall x(F(x)\wedge T(x)\wedge J(x))$
$\forall x(F(x) \to (T(x)\wedge J(x)))$
The second one is correct: if an animal is a frog then it has a long tongue and likes to jump.
The first one says that every animal is a frog and has a long tongue and likes to jump.