# choose from implication and logical and in write assertions in first-order logic

I am a student and I get confused in translating some sentence to logic assertion.

For example: Joe does not have a lawyer, i.e. is not a customer of any lawyer.

The right way to translate is:

"For all $p$, if $p$ is lawyer then Joe is not a customer of $p$"

or

"For all $p$, if $p$ is lawyer ∧ Joe is not a customer of $p$"

What the difference between these two clause?

• The second one is not well-formed at all -- there's an "if" with no matching "then". – Henning Makholm Aug 2 '15 at 19:38