In logic, own symbols are used in order to be able to represent the relations between propositions in a general and independent way to the proposition, in order to be able to find the relationship process that operates in the communicated message, the propositional logic.
For this purpose there are, among others, the following logical operators: conjunction (and) ∧, disjunction (or) ∨, denial (not) ¬, conditional (if - then) ⇒ and double conditional (if and only if, iff) ⇔.
So for this case we have:
Answer
a) Sam had pizza last night if and only if Chris finished her homework.
p⇔q
b) Pat watched the news this morning iff Sam did not have pizza last night.
r⇔¬p
c) Pat watched the news this morning if and only if Chris finished her homework and Sam did not have pizza last night.
r⇔(q∧¬p)
d) In order for Pat to watch the news this morning, it is necessary and sufficient that Sam had pizza last night and Chris finished her homework.
r⇔(p∧q)
e) <em>q ⇔ r</em>
Chris finished his homework if and only if Pat watched the news this morning
f) <em>p ⇔ (q ∧ r)</em>
Sam had pizza last night if and only if Chris finished his homework and Pat watched the news this morning
g) <em>(¬p) ⇔ (q ∨ r)
</em>
Sam didn't have pizza last night if and only if Chris finished his homework or Pat watched the news this morning
h) <em>r ⇔ (p ∨ q)
</em>
Pat watched the news this morning if Sam had pizza last night or Chris finished his homework
is