1. Here we consider sets A, B, C U where U is a universal set.

(a) If AB C determine the relationship between A \ C and A B.

(b) Determine P(A) P(A^c ).

(c) Is P(A) P(A^c) = P(U)?

(d) Is P(A) \ P(B) P(A r B)?

2. Express the following statements in the symbolic language using symbols as instructed in Problem group 1 and then negate the statement. Use only symbols =, <, and arithmetic operations like +, , and similar. In (e) consider a set A Q.

(a) For every real number r the equation 8x + r = 0 has precisely one real solution.

(b) There are at least three different integers in the interval (2, 2).

(c) For every real number x larger than 1 the value 1/x is smaller than 1 but larger than 0.

(d) Between any two distinct integers there is an element of A.