Let the possible variable values be $ \Bbb U = \{true, false\} $. There are no predicates in the following formulae since the variable values already are boolean values. Give the truth value for each interpretation for the following formula:
$ \forall x \forall y: (x \land y) \leftrightarrow \lnot x $
I have no idea how to solve the given problem. Can anyone please help me? Thank you in advance. :)
The problem is a propositional logic problem in disguise : the solution is simply the turth-table of the propositional formula : $(x∧y) ↔ ¬x$.
We can easily check that for $v(x) = v(y)= \text {true}$ the formula is evaluated to $\text {false}$.
Thus, it is not true that $\mathbb U \vDash ∀x \ ∀y \ ((x ∧ y) ↔ ¬x)$.
In the same way, we can check with $v(x)= \text {true}$ that $∃x∀y (x \lor y)$ is true in $\mathbb U$.