can anyone please explain to me how to solve this graph exercise?

Question

Given: A = {1,2,3}, B = {4,5,6} C = {a,b}

Find:

a. A x B b. B x C c. A x C

Given: A = (3,6,9), B = (4,5,6)

a. Find A x B

b. Find the relation that the first component is smaller than the second component.

Answer 1

Typically when working with sets, the x symbol is being used to represent the cartesian product.

For the first one, A x B you would do all the combinations.

{(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)}

B x C

{(4,a),(5,a),(6,a),(4,b),(5,b),(6,b)}

For the second one, you would come up with A x B and then remove all the pairs that don't meet the criteria of the first term being smaller than the second.