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!