Let $P(x),Q(x),R(x)$ be the statements $x$ is a clear explanation,$x$ is satisfactory,$x$ is an excuse,respectively. Suppose that the domain for $x$ consists of all the English text. Express each of these statements using quantifiers, logical connectives and $P(x),Q(x),R(x)$.
a. All clear explanations are satisfactory.
b. Some excuses are unsatisfactory.
c. Some excuses are not clear explanations
Please Corret Me
a. $\forall x ~ (P(x) \to Q(x))$
b. $\exists x ~ (R(x) \to \neg Q(x))$
c. $\exists x ~ (R(x) \to \neg P(x))$
I am not completely sure why I have used implication instead of a conjunction, I am wondering can someone explain,