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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. $∀x[(\text{tiger}(x) ∧ \text{lion}(x)) → {(\text{hungry}(x) ∨ \text{threatened}(x)) → \text{attacks}(x)}]$
  2. $∀x[(\text{tiger}(x) ∨ \text{lion}(x)) → {(\text{hungry}(x) ∨ \text{threatened}(x)) ∧ \text{attacks}(x)}]$
  3. $∀x[(\text{tiger}(x) ∨ \text{lion}(x)) → {\text{attacks}(x) → (\text{hungry}(x) ∨ \text{threatened}(x))}]$
  4. $∀x[(\text{tiger}(x) ∨ \text{lion}(x)) → {(\text{hungry}(x) ∨ \text{threatened}(x)) → \text{attacks}(x)}]$
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Best answer
61 votes
61 votes

The statement $\text{“Tigers and lions attack if they are hungry or threatened"}$ means that if an animal is either tiger or lion, then if it is hungry or threatened, it will attack. So option (D) is correct. 

Do not get confused by $\text{“and"}$ between tigers and lions in the statement. This $\text{“and"}$ does not mean that we will write $\text{“tiger(x) ∧ lion(x)"}$, because that would have meant that an animal is both tiger and lion, which is not what we want.

http://www.cse.iitd.ac.in/~mittal/gate/gate_math_2006.html

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7 votes
7 votes

∀x [ ( Tiger(x) ∨ Lion(x) ) ∧  (Hungry(x) ∨ Threatened(x)) --> Attack(x) ]

We can represent also in this way,bcoz of

Exportation law : (P-->(Q-->R)) ≡ ((P ∧ Q) -->R)

So, D is correct ans. 

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

5 votes
5 votes
For solving these type of questions break the sentence into predicates i.e. p(x)=lions or(not and) tigers q(x)=hungry or threatened r(x) = attack now join them using implication for all x so option d.
1 votes
1 votes

Option D bcz it may be lion or tiger here which attacks and AND is just used as 'OR' option a says they always attack together which is wrong so not option a

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