A Logical Proposal Indeed

A is a shy guy and is not able to gather courage to propose to B. A is also a logician so he takes the help of predicate logic. Now A is trying to make B understand predicate logic, but actually he wants to propose to B. He goes on as following:

Let us first define the predicates.

M(x,y) : x and y marry

L(x,y) : x loves y

A predicate can be true or false. Just to see some properties of the above predicates,

M(A,B) <=> M(B,A)

“I am married to you” means “you are married to me”.

L(A,B) => L(B,A)

This statement is not true. If I love you, then it does not mean that you love me. Hence the predicate on left does not imply the predicate on right.

But now, if I say reverse them, that is

L(B,A) => L(A,B)

This statement is true. This is because whether you love me or not, I will always love you. Hence there cannot be a case where you love me and I don’t love you.

Now we also have,

L(A,B) ^ L(B,A) => M(A,B)

i.e. if I love you and you love me, then we will marry. But now since I always love you, we can remove L(A,B). Thus,

L(B,A) => M(A,B)

Thus if you love me, we will marry.

Do you love me?