Geetha has a conjecture about integers, which is of the form
$$\forall x\left( {P(x) \Rightarrow \exists yQ(x,y)} \right)$$,
where P is a statement about integers, and Q is a statement about pairs of integers. Which of the following (one or more) option(s) would imply Geetha's conjecture?
Choose the correct choice(s) regarding the following propositional logic assertion S:
S : ((P ∧ Q)→ R)→ ((P ∧ Q)→ (Q → R))
Let p and q be two propositions. Consider the following two formulae in propositional logic.
S1 : (¬p ∧ (p ∨ q)) → q
S2 : q → (¬p ∧ (p ∨ q))
Which one of the following choices is correct?
The statement $(\neg p) \Rightarrow(\neg q)$ is logically equivalent to which of the statements below?
I. $\quad p \Rightarrow q$
II. $q \Rightarrow p$
III. $(\neg q) \vee p$
IV. $(\neg p) \vee q$