Discrete Mathematical Structures by Pearson

1-6 Discrete Mathematical Structures

A ∩ B is shaded.

(A ∩ B)′ is area other than shaded.

More generally, the intersection of sets A

1

, A

2

,…, A

n

is denoted by,

A

1

∩ A

2

∩ … ∩ A

n

= A

i

i

n

=1



= {x: x ∈ A

i

for each i}, that is, the set of all elements that belong

to each of them.

Examples

1. If A = {1, 2, 3} and B = {2, 3, 4, 5, 6}, then A ∪ B = {1, 2, 3, 4, 5, 6} and A ∩ B = {2, 3}.

2. If A = {a, b, c} and B = {x, y, z}, then A ∪ B = {a, b, c, x, y, z} and A ∩ B = F.

3. If A = {x: x is a multiple of 2} and B = {x: x is a multiple of 5}, then A ∩ B = {x: x is a

multiple of 2 and 5 both} = {x: x is a multiple of 10}.

Difference of Two Sets

Let A and B