1) Use the following propositions (30 points):
p: I will wear my lucky hat.
q: My team will win tonight.
to write the following statements in terms of p, q, and logical connectives (~, ?, ?, ?, and ?). Which of these, if any, are equivalent to each other? Explain your answers.
a) If I wear my lucky hat, then my team will win tonight. p ? q p then q conditional statement.
b) My team will win tonight only if I wear my lucky hat. ~p ? ~q this is a converse statement.
c) If I do not wear my lucky hat, then my team will not win tonight. ~(p ? q) contrapositive implication.
d) Wearing my lucky hat is a sufficient condition for my team to win tonight.
p ? q, p is sufficient for q. implication
a is equivalent to d, and b is equivalent to c.
B and C are wrong and im not sure why and what the correct answer is. Thank you in advance for your assistance!
