Page 31 - Discrete Structure II

A binary relation from A to B is a subset of A x B

Example 2:

Consider the following A ={a, b} B = { a, c, d}, C = {1, 2}

Find A x B x C and C x A x B
Solution

A x B X C consists of all triplets (x, y, z ) such that x is an element of A , y is an element of B and z is an
element of C.

A x B X C ={(a, a, 1), (a, c, 1), (a, d, 1), (b, a, 1), (b, c, 1), (b, d, 1), (a, a, 2), (a, c, 2), (a, d, 2), (b, a, 2), (b, c,
2), (b, d, 2)

Exercises:

a. Determine how many times “Discrete II” is printed

for ( i =1; i < 5; i++)

for ( j =1; j <= 5; i++)

for ( k =1; k < 4; k++)

print (“Discrete II”);

Answer: 60 times

for ( i =1; i < 5; i++) A={1, 2, 3, 4}

for ( j =1; j <= 5; i++) B = { 1, 2, 3, 4, 5}

for ( k =1; k < 4; k++) C = {1, 2, 3}

|A x B x C | = 4 x 5 x 3 = 60

b. Determine how many times “Discrete” is printed