Let

M

$($

x

$,$

y

$)$

be $$

x

$$

y

$>$

$0$

$,$

G

$($

x

$,$

y

$)$

be $$

x

$>$

y

$$ and

N

$($

x

$)$

be $$

x

$<$

$0$

$.$ Let the domain be $\{100,99,98,...,98,99,100\}.$

Select the correct Translation and decide its truth value of the statment.

$$

x

$$

$!$

y

$($

G

$($

x

$,$

y

$)$

$->$

$($

M

$($

x

$,$

y

$)$

$$

N

$($

x

$)$

$)$

$)$

Let

M

$($

x

$,$

y

$)$

be $$

x

$$

y

$>$

$0$

$,$

G

$($

x

$,$

y

$)$

be $$

x

$>$

y

$$ and

N

$($

x

$)$

be $$

x

$<$

$0$

$.$ Let the domain be $\{100,99,98,...,98,99,100\}.$

Select the correct Translation and decide its truth value of the statment.

$$

x

$$

$!$

y

$($

G

$($

x

$,$

y

$)$

$->$

$($

M

$($

x

$,$

y

$)$

$$

N

$($

x

$)$

$)$

$)$

Translation: For all

x

there exists some

y

such that,

x

being greater than

y

implies that their difference is greater than zero and

x

is positive. Truth value: False.

Translation: For all

x

there exists a unique

y

such that,

x

minus a

y

is greater than zero, or

x

is less than zero if

x

is greater than that unique

y

$.$ Truth value: False

Translation: There exists some

x

and

y

where

x

is greater than

y

implies that their difference is greater than zero or

x

is negative. Truth value: True

Translation: For exactly one

y

$,$ it is true that for all

x

such that the difference between them is positive only if

x

is negative and

x

is greater than

y

$.$ Truth value: False