Multiple choice

Which one of the first order predicate calculus statements given below correctly expresses the following English statement? Tigers and lions attack if they are hungry or threatened.

  1. ∀x[(tiger(x) ∧ lion(x)) → {(hungry(x) ∨ threatened(x)) → attacks(x)}]

  2. ∀x[(tiger(x) ∨ lion(x)) → {(hungry(x) ∨ threatened(x)) ∧ attacks(x)}]

  3. ∀x[(tiger(x) ∨ lion(x)) → {attacks(x) → (hungry(x) ∨ threatened(x))}]

  4. ∀x[(tiger(x) ∨ lion(x)) → {(hungry(x) ∨ threatened(x)) → attacks(x)}]

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The given statement can be explained as follows: If x is lion or if it is hungry or it is threatened, x will attack P(x) = lion (x) v tiger (x) Q(x) = hungry (x) v threatened (x) R (x) = attacks (x) P(x) $\rightarrow$ (Q (x) $\rightarrow$ R (x)) Expanding all, ∀x[(lion(x) ∨ tiger(x)) → {(hungry(x) ∨ threatened(x)) → attacks(x)}]