Logical Equivalences Involving Biconditional Statements.
p ↔ q ≡ (p → q) ∧ (q → p)
p ↔ q ≡ ¬p ↔¬q ( option 2)
p ↔ q ≡ (p ∧ q) ∨ (¬p ∧¬q) (option 3)
Logical Equivalences Involving Conditional Statements
p → q ≡ ¬p ∨ q
p → q ≡ ¬q →¬p
¬(p → q) ≡ p ∧¬q
(p → q) ∧ (p → r) ≡ p → (q ∧ r)
(p → r) ∧ (q → r) ≡ (p ∨ q) → r ( option 1)
(p → q) ∨ (p → r) ≡ p → (q ∨ r)
(p → r) ∨ (q → r) ≡ (p ∧ q) → r (in option 4 there is and instead of or ) hence correct ans is 4
(we can always check via truth tables or by removing --> and <-> if above formulas are not learned properly)