GATE CSE 2006 | Question: 26

Question

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.

• A. $∀x[(\text{tiger}(x) ∧ \text{lion}(x)) → {(\text{hungry}(x) ∨ \text{threatened}(x)) → \text{attacks}(x)}]$
• B. $∀x[(\text{tiger}(x) ∨ \text{lion}(x)) → {(\text{hungry}(x) ∨ \text{threatened}(x)) ∧ \text{attacks}(x)}]$
• C. $∀x[(\text{tiger}(x) ∨ \text{lion}(x)) → {\text{attacks}(x) → (\text{hungry}(x) ∨ \text{threatened}(x))}]$
• D. $∀x[(\text{tiger}(x) ∨ \text{lion}(x)) → {(\text{hungry}(x) ∨ \text{threatened}(x)) → \text{attacks}(x)}]$

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Detailed Video Solution: GATE CSE 2006 | Question: 26

Answer 1

The above statement means that if the animal is either a Tiger or a lion and if he is hungry or is threatened then it will attack. Here if the animal is not tiger or a lion we will not care about it i.e., if $[(\text{tiger}(x) ∨ \text{lion}(x))$  is false then will not care about the value of the RHS. So, RHS may be true or false so $false→false/true$  is taken ans true . so, there will be $∀x[(\text{tiger}(x) ∧ \text{lion}(x)) →$

Now "if they are hungry or threatened" means the RHS should be ${(\text{hungry}(x) ∨ \text{threatened}(x)) → \text{attacks}(x)}$ 

so, option (D) is correct i.e., $∀x[(\text{tiger}(x) ∧ \text{lion}(x)) → {(\text{hungry}(x) ∨ \text{threatened}(x)) → \text{attacks}(x)}]$

Answer 2

The statement "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 "and" between tigers and lions in the statement.

 

This "and" doesn't mean that we will write "tiger(x) ∧ lion(x) ", because that would have meant that an animal is both tiger and lion, which is not what we want.

hope my answer helps u a lot

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