Please choose the correct option$($s$)$ for each question and provide a detailed justification or reasoning for your selected option or answer.

I will equally provide feedback and a detailed explanation of your answer, whether it is correct or in$-$correct.

Question $1$

In this question, assume the following specifications:

$F(x,y)$ : $x$ is the father of $y$

$M(x,y)$:$x$ is the mother of $y.$

Which of the formulas in predicate logic below express the sentence 'Everybody has a mother?

A$.$ AAxAAyM$(x,y)$

B$.$ EExAAyM$(x,y)$

C$.$ EEyAAxM$(x,y)$

D$.$ AAxEEyM$(x,y)$

E$.$ AAyEExM$(x,y)$

Question $2$

In this question, assume only the specifications:

$F(x,y)$:$x$ is the father of $y$

$M(x,y)$:$x$ is the mother of $y.$

Which of the formulas in predicate logic below express the sentence 'Anyone who is a father is not a maternal grandmother?

A$.$ AAx$(EEyF(x,y)$notEEyEEz$(M(x,y{)}^{{?}^{?}}M(y,z)))$

B$.$ AAx$(EEyF(x,y)$notEEyM$(x,M(y)))$

C$.$ AAx$(EEyF(x,y)$notEEyG$(x,y))$

D$.$ EExEEyF$(x,y)$notEExEEyM$(x,y)$

E$.$ EEx$(F(x)$notM$(M(x)))$