How to read predicate formulas

Question

I have just started learning about predicate logic and am having some trouble in figuring out how to actually read the formula as as a sentence.

¬(marriedTo(X , Y ) ⇒ marriedTo(Y , X ))

Would I read the above formula as;

if X is not married to Y, the Y is married to X

?

Answer 1

According to the grouping of terms, the negation operator acts on the entirety of the implication $$\mathop{\mathrm{marriedTo}}(X,Y) \rightarrow \mathop{\mathrm{marriedTo}}(Y,X).$$

The above formula can be translated as:

If X is married to Y, then Y is married to X.

Therefore, the negation of that formula, $$\neg(\mathop{\mathrm{marriedTo}}(X,Y) \rightarrow \mathop{\mathrm{marriedTo}}(Y,X)),$$ can be translated as:

It is not the case that if X is married to Y then Y is married to X.

In other words, the formula in question asserts that $X$ being married to $Y$ does not guarantee $Y$ is married to $X$. The predicate $\mathop{\mathrm{marriedTo}}$ is, therefore, not symmetric.