I have the following question:
And I have drawn up the truth table below:
My question is I see there is one truth value that both the premise and conclusion have in common, but does that mean that the premise does or does not entail the conclusion? Thanks for any help!
No, we cannot conclude this. I'm afraid of confusing you with formalism.. but I better explain it in details. In usual terminology, entailment in the propositional calculus is defined this way: let $\Gamma$ be a set of formulae and $\phi$ a formula. We say that $\Gamma$ entails $\phi$ iff for any valuation $v$, if $v(\psi)=1, \psi \in \Gamma$ then $v(\phi)=1$ (Roughly speaking, whenever all formulae in $\Gamma$ are true, $\phi$ must be true). This is why it's always better, when working with truth tables, to just check the lines all premises are true and see if in any of those lines the conclusion is false. If it's not the case, we say the premises entail the conclusion.