Question

Let A = {a, b, c, d, e}, B = {a, b, e}, C = {d, e, f}, and U= {a, b, c, d, e, f}. List the elements of: a. B times C b. C times C^c

Answer 1

X is known as cartesian product. Cartesian product of the two non empty Sets P, Q is defined as the set of ordered pairs (x,y) such that x ∈ P and y ∈ Q

Given sets
A = {a, b, c, d, e};
B = {a, b, e};
C = {d, e, f};

Universal set U = {a, b, c, d, e, f};

a. AXB is

{(a,a),(a,b},(a,e),(b,a),(b,b),(b,e),(c,a),(c,b),(c,e),(d,a),(d,b),(d,e),(e,a),(e,b),(e,e)}

b. CXC^

C^ also known as the complement of set C is defined as the set of elements that are in the universal set U, but not in C

C = {d,e,f};
C^ = U-C = {a,b,c};

CXC^ = {(a,d),(a,e),(a,f),(b,d),(b,e),(b,f),(c,d),(c,e),(c,f)}