Symbolize each of the following arguments in proportional lo

Symbolize each of the following arguments in proportional logic (giving an explicit scheme of abbreviation), then use one of the truth table methods (direct or indirect) to determine whether it is valid or invalid. If invalid, assign truth values to the sentence letters to prove it is invalid, and if valid, prove the argument valid by the method of deduction. (a) Bart is allowed to go out, if and only if be is not grounded. Bart will go to the birthday party, unless lie is grounded. If Bart gets in trouble, be will be- grounded, Therefore, it Bart gels in trouble, he will not go to the birthday party.

Solution

p:bart is allowed to go out

q: bart is grounded

r: bart will go to the bday party

s: Bart gets in trouble;

p and ~ q;

r and ~ q;

s and q;

s and ~r;