Predicate

Question

Every Indian has his own dreams.

$\forall x \exists y[I(x)\rightarrow D(y)\wedge H(x,y)]\\ \forall x \exists y[I(x)\wedge D(y)\rightarrow H(x,y)]\\$

here, H(x,y) is x has y

which is true?

Comments

^ here conjunction.

And I think, first one should be ans..because if x is an Indian then there is a dream y and x has dream y ??

2nd one says - If x is an Indian and there is a dream Y then x has dream Y.

??

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Yes, I correct myself. Now, even I think 1st one because of following:

Indian or not                Dream or not               Has(x,y)

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

Indian                          no                                  no

                                   no                                   yes

                                  yes                                 no

 

Now, 2nd query will select this Indian while 1st query will not. Now, if the 2nd query selects this tuple, it contradicts the statement "Every Indian has his own dream".

Hence, only 1st query.

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It is just a modification of previois year gate question. Second one says every person is an Indian definately false.

First one isanswer(true).

Answer 1

1.  $\forall x \exists y[I(x)\rightarrow D(y)\wedge H(x,y)]$

Eng Translation:- For all if he is Indian then there exist some dream and he has that dream.
which is equal to "Every Indian has his own dream"

2. $ \forall x \exists y[I(x)\wedge D(y)\rightarrow H(x,y)]\\$

Eng Translation:- For all x and some y, if x is Indian and y is dream then x has that dream y.
Its sound like "Every Indian has some specific dream"