Let p be the proposition “I will do every task in this list” and q be the
proposition “I will get an award.” Express each of these as a combination of p and
q.
(a) Either I will not get an award or I will not do every task in this list.
(b) I will get an award only if I do every task in this list.
(c) For me to get an award it is necessary and sufficient that I do every task in this list.
This is what I got for each one. I am not fully certain about my answers.
(a) ¬q V ¬p
(b) q -> p
(c) q <-> p
Your answers are correct!
(a) ¬q V ¬p: This translates to "Either I will not get an award or I will not do every task in this list." It is a disjunction where either "I will not get an award (¬q)" or "I will not do every task in this list (¬p)" is true.
(b) q -> p: This translates to "I will get an award only if I do every task in this list." It is an implication where if "I will get an award (q)" is true, then "I will do every task in this list (p)" must also be true.
(c) q <-> p: This translates to "For me to get an award it is necessary and sufficient that I do every task in this list." It is a biconditional where "I will get an award (q)" is true if and only if "I will do every task in this list (p)" is true.