Find the truth value of the compound proposition when 𝑝=𝑟=𝑞= True. (𝑟⟷𝑝)∧¬𝑞Group of answer choicesTrueFalse

The given compound proposition is (𝑟⟷𝑝)∧¬𝑞.

Step 1: Substitute the given values of p, q, and r into the compound proposition. All of them are True. So, the proposition becomes (True ⟷ True) ∧ ¬True.

Step 2: The biconditional (⟷) operator returns True if both the operands are identical. Here, both are True. So, (True ⟷ True) becomes True. Now, the proposition becomes True ∧ ¬True.

Step 3: The negation (¬) operator flips the truth value of the operand. Here, ¬True becomes False. So, the proposition becomes True ∧ False.

Step 4: The conjunction (∧) operator returns True if both the operands are True. Here, one operand is False. So, True ∧ False becomes False.

Therefore, the truth value of the given compound proposition is False.