Which one of the first order predicate calculus statements given below…

Correct formalization: ∀x[(tiger(x) ∨ lion(x)) → ((hungry(x) ∨ threatened(x)) → attacks(x))]

Explanation:

• Universal quantifier ∀x ensures the statement applies to all individuals.

• The antecedent (tiger(x) ∨ lion(x)) matches the English "Tigers and lions" meaning "either a tiger or a lion."

• The inner implication (hungry(x) ∨ threatened(x)) → attacks(x) directly captures "attack if they are hungry or threatened": being hungry or threatened implies attacking.

Why the other formalizations are incorrect:

• A formula using (tiger(x) ∧ lion(x)) as the antecedent is wrong because it requires an individual to be both a tiger and a lion.

• A formulation with the consequent (hungry(x) ∨ threatened(x)) ∧ attacks(x) is wrong because it asserts attacks(x) whenever the subject is a tiger or lion, rather than making attacks conditional on being hungry or threatened.

• A formulation with attacks(x) → (hungry(x) ∨ threatened(x)) reverses the implication: it states attacking implies being hungry or threatened, which is the opposite of the intended meaning.

Therefore the correct translation is the one that uses a universal quantifier, a disjunction for tiger or lion, and an inner implication where hungry or threatened implies attacks.