Let ⊕ and bigotimes are two mathematical operators. If p⊕(q bigotimes r) is equivalent to ((p ∧ q) ⇒ r) , then ⊕ and bigotimes

Question

Let ⊕ and bigotimes are two mathematical operators. If p⊕(q bigotimes r) is equivalent to ((p ∧ q) ⇒ r) , then ⊕ and bigotimes (A) can be ∨ and ∧ respectively (B) can be ∧ and ∨ respectively (C) can both be ⇒  (D) can be ⇒ and Leftrightarrow respectively

Tardigrade Admin · Accepted Answer

(p ∧ q)⇒ r Solution

(A) p∨ (.q∧ r.) Solution

(A) is incorrect option (B) p∧ (q ∨ r) Solution

(B) is incorrect option (C) p⇒ (q ⇒ r) Solution

(C) is correct option (D) p⇒ (q Leftrightarrow r) Solution

(D) is incorrect option

Q. Let $\oplus$ and $⨂$ are two mathematical operators. If $p \oplus (q ⨂ r)$ is equivalent to $((p \land q) \Rightarrow r)$ , then $\oplus$ and $⨂$

can be $\lor$ and $\land$ respectively

can be $\land$ and $\lor$ respectively

can both be $\Rightarrow$

can be $\Rightarrow$ and $\Leftrightarrow$ respectively

$(p \land q) \Rightarrow r$
$(A)$ $p \lor (q \land r)$ $(A)$ is incorrect option
$(B)$ $p \land (q \lor r)$ $(B)$ is incorrect option
$(C)$ $p \Rightarrow (q \Rightarrow r)$ $(C)$ is correct option
(D) $p \Rightarrow (q \Leftrightarrow r)$ $(D)$ is incorrect option

Q. Let ⊕ and ⨂ are two mathematical operators. If p⊕(q⨂r) is equivalent to ((p∧q)⇒r) , then ⊕ and ⨂

can be ∨ and ∧ respectively

can be ∧ and ∨ respectively

can both be ⇒

can be ⇒ and ⇔ respectively