If p and q are true and r and s are false statements, then which of the following is true?

Question

If p and q are true and r and s are false statements, then which of the following is true? (A) (q ∧ r)∨ (∼ p ∧ s) (B) (∼ p arrow q) rightarrow (r ∧ s) (C) (p arrow q) ∨ (r rightarrow s) (D) (p ∧ ∼ r)∧ (∼ q ∨ s)

Tardigrade Admin · Accepted Answer

We have statements p, q arrow T and r, s arrow F Option (a) (q ∧ r) ∨(∼ p ∧ s) ≡(T ∧ F) ∨(F ∧ F) ≡ F ∨ F ≡ F Option (b) (∼ p arrow q) rightarrow(r ∧ s) ≡(p ∨ q) arrow(r ∨ s) (∵ p arrow q ≡ ∼ p ∨ q) ≡(∼ p ∨ q) ∨(r ∧ s) ∧((p ∨ q) ∨(∼ r ∧ s))) (∵ p rightarrow q ≡(∼ p ∨ q) ∧(p ∨-q)) ≡(∼(T ∨ T) ∨(F ∧ F) ∧((T ∨ F) ∨(∼(F ∧ F))) ≡(F ∨ F) ∧(T ∨ T) ≡ F ∧ T ≡ F Option (c) (p arrow q) ∨(r rightarrow s) ≡(∼ p ∨ q) ∨((∼ r ∨ s) ∧(r ∨ ∼ s))(∵ p arrow q ≡ ∼ p ∨ q) ≡(F ∨ T) ∨((T ∨ F) ∧(F ∨ T)) ≡ T ∨(T ∧ T) ≡ T . ∨ T ≡ T Option (d) do similar as option (a).

Q. If $p$ and $q$ are true and r and s are false statements, then which of the following is true?

$(q \land r) \lor (\sim p \land s)$

$(\sim p \to q) \leftrightarrow (r \land s)$

$(p \to q) \lor (r \leftrightarrow s)$

$(p \land \sim r) \land (\sim q \lor s)$

Q. If p and q are true and r and s are false statements, then which of the following is true?

(q∧r)∨(∼p∧s)

(∼p→q)↔(r∧s)

(p→q)∨(r↔s)

(p∧∼r)∧(∼q∨s)

Q. If $p$ and $q$ are true and r and s are false statements, then which of the following is true?

$(q \land r) \lor (\sim p \land s)$

$(\sim p \to q) \leftrightarrow (r \land s)$

$(p \to q) \lor (r \leftrightarrow s)$

$(p \land \sim r) \land (\sim q \lor s)$