Question $3$

For this question and question $4,$ assume the specifications below:

The predicate symbols:

$S(x,y)$:$x$ is y$\text{'}$s sister

$B(x,y)$:$x$ is $y\text{'}$s brother

$H(x,y)$:$x$ is $y\text{'}$s husband and

$O(x,y)$:$x$ is older than $y$

and the constant symbols

$j$: John,

c: Carl, and

$m$ : Monique.

Which of the following formulas express the sentence 'Carl is Moniques brother$-$inlaw?

A$.B(c,m{)}^{{?}^{?}}H(c,m)$

B$.B(c,m)vvH(c,m)$

C$.)=(y$

D$.$ EEx$((S(x,m{)}^{{?}^{?}}H(c,x))vv(H(x,m{)}^{{?}^{?}}B(c,x)))$

E$.$ None of the above

Question $4$

Assuming the same specifications as for question $3,$ which of the following sentences are expressed by the following predicate logic formula:

AAxAAy$(S(x,j{)}^{{?}^{?}}S(y,j)O(x,y))$

A$.$ John has an older sister

B$.$ All of John's sisters are older than him

C$.$ John is older than his sisters

D$.$ One of John's sisters is older than another

E$.$ None of the above