a) A football manager has four players, (A,B,C,D), compete for two positions. He has the following five requirements on who gets to play.

Either A or B must play, but not both.

If C does not play, then D must play.

Either both B and C play, or neither of them play.

If D plays, then C does not play.

If B does not play, then C and D play.

Express each of the five requirements in propositional logic. Let for example "A plays", be denoted by A.

b) Using the five propositions as premises, conclude which two players get to play for the team.

c) Determine the truth values of the statements xy(x^2 = y) and xy(x = y^2 ), where the domain is the set of real numbers.