Gate Academy

Question

Which of the following is valid first order formula?

Comments

Is it D)all of the above ?

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no. Given ans is B.
A is definitely wrong, but why isn't C a right option?

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let P(x,y) means " x likes y"

$\exists (y)\exists (x)(P(x,y))$ $\rightarrow$ $\exists (x)\exists (y)(P(x,y))$

$\exists (y)\exists (x)(P(x,y))$ means "someone is liked by someone"

$\exists (x)\exists (y)(P(x,y))$ means "someone like someone".

now you can easily see that first is implying second, actually both RHS and LHS are equivalent statements.

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@Saikat Dutta How A is wrong?

Answer 1

a is not valid.

b and c valid.

Comments

Where did you get this arrow diagram from?