(1) Let X = [7, 4], Y = (%,8). Find the following sets, and express them as an interval, a union of intervals, at nite list or the empty set 9*). (Use R as the universal set, when computing complements in this question.) (2) Let A,B be sets. Prove that if (A F] B)C 2 A6 then A \\ B = q). (3) Negate the following sentence, without using \"negative\" words (e.g. no, none, not,...). \"There is a. student taking MAT 137 at UTM who has no friends whose rst name and last name beginning with P.\" (4) Given a conditional statement \"A => B\" its contrapositive is the statement \"B => m4\". Consider the statement: \"If it's raining, then it's cloudy." Its contrapositive is the statement: \"If it's not cloudy, then it's not raining.\" Explain in your own words why these two statements are equivalent to each other. (5) Write the contrapositive of the following statement. \"If no student in MAT 137 fails the test, then every instructor will get a bonus.\