Propositional Logic Ques no 22

Question

Comments

∃x (M(x) ∧ (∀y F(y) → E(x,y)))

Answer 1

@Devshree. Lets consider option B.

Let the set be S={Ashok, Gauri, Aboli }. Now, I want to state that Ashok earns more all the females.

Now, we are considering only all such males that earn more than all the females.

Now, see the condition Vy ( female(y) ^ more(x,y) ). Here, you need to check both the conditions for Ashok. Instead, I should be checking only if the other person is female. If the other person is female, then necessarily, ashok earns more than her. I should not  need to check if he is actually earning more than her.

SO, the second clause should be like Vy ( female(y) $\rightarrow$ more(x,y) )

Comments

@sushant...Here we are saying (Vy ( female(y) ^ more(x,y) )) ...all the employees are female which is not possible.
Correct me if i m wrong.

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NO, i am saying that if we are using Vy female(y) without checking any condition, it means that there are only females, which is not possible.

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@Vaishali. You arent right

Vy [ females(y) ] means domain of females. So, if there exists employee table, then what this says is consider all female employees. It doesnt say all are females.

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@Vaishali. Rather consider this sql table and check where the 2nd option will return true.

Table Employees:

Name    Earns

-----------------------

Sushant   20/-

Anish       40/-

Vaishali   10/-

Aboli         30/-

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So, I think option 2 is correct if we consider above sql table.

Answer 2

OPTION B as for there exists we use "AND" , not implication...

Comments

Thanks for the answer. Could you be specific with the explanation portion too as to why the answer B?

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see this...

https://gateoverflow.in/1020/gate2004_23

you'll understand...

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actually it should be female(y)--->more(x,y)

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debanjan sarkar why?