Let
p = Ram goes to picnic.
q = Shyam goes to picnic.
r = Radha goes to picnic.
s = Sita goes to picnic.

Then the statement \”Ram, Sita, and Radha go to picnic if and only if Shyam doesn’t go to the picnic, but if neither Ram and Sita go to the picnic, then Shyam go to picnic only if Radha goes.\” is represented by

(A) (p ∧ r ∧ s → ¬q) ∧ (p ∧ s) → (q → r)
(B) (p ∧ r ∧ s → ¬q) ∨ (p ∧ s) → (q → r)
(C) (p ∧ r ∧ s ↔ ¬q) ∨ (p ∧ s) → (q ↔ r)
(D) (p ∧ r ∧ s ↔ ¬q) ∧ (¬p ∧ ¬s) → (q → r)


Answer: (D)

Explanation: (p and r and s if and only if ¬q) ∧ (¬ and ¬s) → (q only if r) = (p ∧ r ∧ s ↔ ¬q) ∧ (¬p ∧ ¬s) → (q → r)

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