I need to know if $P→(Q∧R)$ is the correct answer to this?
$P =$ you can vote
$Q =$ you are under 18 years old
$R =$ you are from mars
Based on the above information, construct the formal-logic statement for the following English statement:
You cannot vote if you are under 18 years old or you are from Mars
No, not correct.
Your statement says: if you can vote, then you are under 18 years old, and you are from Mars ... which is clearly not what we want. This would mean that for whomever comes out of the voting booth, we can claim that they are under 18 years old, an are from Mars!
The direct translation would be:
$(Q \lor R) \rightarrow \neg P$
by Contraposition that is equivalent to:
$P \rightarrow \neg (Q \lor R)$
and by DeMorgan that is equivalent to:
$P \rightarrow (\neg Q \land \neg R)$
Another way of thinking about this is: Being 18 years or older, and not being from Mars are necessary conditions in order to vote. So, if you are some who can vote, then we know that you are 18 years or older and not from Mars .