I was asked to prove the above. The teacher has assured me that they are indeed equivalent, but when drawing a truth table, I have not been able to show this.
$P =$ F,
$Q =$ T,
$R =$ T.
I have the first portion as true but the second as false.
Would someone be able to confirm whether I have made an error or not?
If it my assertion is indeed wrong and I have messed up somewhere, please do not show me the final proof, as I do want to work it out, but just want to ensure that it is actually provable.
Thanks in advance
Thank both for your help. I just had one final question on the topic regarding semantics
for $$ P \land Q \Rightarrow R $$
JMoravitz, based on your answer, I suppose it should be treated as $$ (P \land Q) \Rightarrow R$$ as opposed to how I was originally viewing the problem$$P\land (Q \Rightarrow R)$$ I'm assuming that everything before an implication should ALWAYS be grouped together? Should everything after the implication also be grouped together regardless of what follows?
if not, how would you go about determining grouping?