in Mathematical Logic edited by
6,339 views
43 votes
43 votes

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. $∀x[(\text{tiger}(x) ∨ \text{lion}(x)) → {(\text{hungry}(x) ∨ \text{threatened}(x)) → \text{attacks}(x)}]$
in Mathematical Logic edited by
6.3k views

5 Answers

47 votes
47 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. 

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

edited by
by

4 Comments

Why option B is wrong
0
0
Also, q if p type of clause in the statement given makes option (C) incorrect.
3
3
6 votes
6 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.
by
1 vote
1 vote

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

2 Comments

Here "AND" means an animal is both tiger and lion, which is not what we want.
0
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
0
0
Answer:

Related questions