logical-equivalence

Let p and q be two propositions. Consider the following two formulae in propositional logic. S 1 : (¬p ∧ (p ∨ q)) → q S 2 : q → (¬p ∧ (p ∨ q)) Which one of the following choices is...

Choose the correct choice(s) regarding the following propositional logic assertion S: S : ((P ∧ Q)→ R)→ ((P ∧ Q)→ (Q → R))

Which one of the following predicate formulae is NOT logically valid? Note that W is a predicate formula without any free occurrence of x .

Let $$p,q,r,s$$ represent the following propositions. $$p:\,\,\,x \in \left\{ {8,9,10,11,12} \right\}$$ $$q:\,\,\,x$$ is a composite number $$r:\,\,\,x$$ is a perfect square $$s:\,...

Which one of the following is NOT logically equivalent to $$\neg \exists x\left( {\forall y\left( \alpha \right) \wedge \left( {\forall z\left( \beta \right)} \right)} \right)?$$

$$P$$ and $$Q$$ are two propositions. Which of the following logical expressions are equivalent? $${\rm I}.$$ $${\rm P}\, \vee \sim Q$$ $${\rm I}{\rm I}.$$ $$ \sim \left( { \sim {\...

Which of the following tuple relational calculus expression(s) is/are equivalent to $$\forall t \in r \left(P\left(t\right)\right)$$? I. $$\neg \exists t \in r \left(P\left(t\right...

Let Graph$$(x)$$ be a predicate which denotes that $$x$$ is a graph. Let Connected$$(x)$$ be a predicate which denotes that $$x$$ is connected. Which of the following first order l...

Consider the relation employee(name, sex, supervisorName) with name as the key, supervisorName gives the name of the supervisor of the employee under consideration. What does the f...

Consider the following propositional statements: $${\rm P}1:\,\,\left( {\left( {A \wedge B} \right) \to C} \right) \equiv \left( {\left( {A \to C} \right) \wedge \left( {B \to C} \...

Let $$a(x,y)$$, $$b(x,y)$$ and $$c(x,y)$$ be three statements with variables $$x$$ and $$y$$ chosen from some universe. Consider the following statement: $$$\left( {\exists x} \rig...

Let $$a, b, c, d$$ be propositions. Assume that the equivalences $$a \leftrightarrow \left( {b \vee \neg b} \right)$$ and $$b \leftrightarrow c$$ hold. Then the truth value of the...