DMGT question

Question

Answer 1

Please see the above properties . All are correct.So option D should be the correct option

Comments

nice explaination

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@Habib...I think A can be bi-conditional also but not B!!
Is B true in the otherway?

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Forget about ∃_x  ..Then according to ur query the predicate reduces to :

∃_y P(y)  ==> ∀_y P(y)

which is not at all true..

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Yes..

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@Habibkhan How 3rd point in your notes is true... Can you explain a bit?

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In 3rd point the LHS means that "there exists y for all x" means it is pointing to a particular value of y irrespective of value of x meaning independent behaviour but rhs side means "for all x there exists y" meaning that given a x there exists a value y but not necessarily the same value y..

That is why the given implication is one way true only..It is not biconditional..

Answer 2

D)all of the above are correct valid first  order formulae