Problem 18.5

Let A = {2, 4} and B = {6, 8, 10} and define the binary relations R and S from A to B as follows:(x, y) A B,(x, y) R x|y.(x, y) A B, x S y y 4 = x.

List the elements of A B, R, S, R S, and R S.

Problem 18.6

Consider the binary relation on IR defined as follows:

x, y R, x R y x y.

Is R reflexive? symmetric? transitive?

Problem 18.7

Consider the binary relation on IR defined as follows:x, y R, x R y xy 0.

Is R reflexive? symmetric? transitive?

Problem 18.8

Let = {0, 1} and A = . Consider the binary relation on A defined as follows: x, y A, x R y |x| |y|,where |x| denotes the length of the string x. Is R reflexive? symmetric?transitive?

Problem 18.9

Let A 6= and P(A) be the power set of A. Consider the binary relation on P(A) defined as follows:X, Y P(A), X R Y X Y.Is R reflexive? symmetric? transitive?