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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[(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)}]
asked in Mathematical Logic by Active (3.7k points)
edited by | 1.4k views

5 Answers

+23 votes
Best answer

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. 
Don't get confused by $\text{"and"}$ between tigers and lions in the statement. This $\text{"and"}$ doesn't 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

answered by Loyal (5.9k points)
edited by
0

can you please explain the difference between (C) and (D)

+6
It has been said that tiger and lion attack if they are hungry or threatened.
It means if they are hungry or threatened, they will attack. But if they are not, they may or may not attack(nothing is said about this). In option (C) , it is attack(x)->(hungry(x) or threatened(x)) , this is not true , as if attack(x) is true, the 2nd part has to be true, i.e. they HAVE to be hungry or threatened, which is not correct. Hence D is the correct choice
0
Thanks dude, that clears it.
0

∀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)

0
I am unable to differentiate between option B and D :(
+4 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.
answered by Active (3.3k points)
+3 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)}]

answered by Loyal (6.2k points)
+1 vote
option D
answered by Active (2.7k points)
0 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

answered by Loyal (6.4k points)
0
Here "AND" means an animal is both tiger and lion, which is not what we want.
0
tiger and lion attack if they are hungry or threatened.
This can be written as

(tiger and lion ).   (attack )if (they are hungry or threatened.)

(anything in the world if is is tiger v lion ) (attack ) if ( hungry or threatened)

 (attack ) if ( hungry or threatened) is q if p form hence p->q

if ( hungry or threatened)->(attack) rest is simple


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