Let S 0 1 2 3 4 and T 0 2 4 How many elements are there in

Let S = {0, 1, 2, 3, 4} and T = {0, 2, 4} How many elements are there in S times T? List or draw the elements in the set {{m, n) epsilon S times T: m

(a) Given that S = { 0,1,2,3,4} and T = { 0,2,4}

clearly n(S) = 5 and n(T) = 3 so that n(SxT) = n(S) x n(T) = 5 x 3 = 15

That is S x T = { (0,0),(0,2),(0,4),(1,0),(1,2),(1,4),(2,0),(2,2),(2,4),(3,0),(3,2),(3,4),(4,0),(4,2),(4,4) }

(b) Now the elements (m,n) of S x T such that m < n are

{ (0,2),(0,4),(1,2),(1,4),(2,4),(3,4) }