Question

For the following open sentence, the universe of discourse is
**N**, the set of natural numbers. What does the
statement about the open sentence mean? Also state whether the
statement is true or false:

Open
Sentence: *T*(*x*,
*y*) : *xy* is even.

Statement:
∃!*x*∀*y T*(*x*, *y*).

There exist an *x* such that for all
*y, *the product *xy* is even. (False)

For all *x* and *y*, the product
*xy* is even. (True)

For all *y* , there exist a
unique *x*, such the product *xy* is even.
(False)

There exist *x* and *y*, such that the
product *xy* is even. (True)

None of the above

Answer #1

What does the statement about the open sentence mean?Also state whether the statement is true or false:

Answer :- The correct answer is , **None of the
above**

Explanation:

The correct meaning of the statement about the open sentence is:
For all *y* , there exist a
unique *x*, such the product *xy* is
even.

For an example , take x=2 , so when y= 1, xy = 2*1 =2

y=2, xy = 2*2=4

y=3, xy = 2*3=6 and so on.

So the statement that **For all y ,
there exist a unique x, such the product
xy is even** is actually TRUE. But , it is gven as
false. So we have choosen

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