Page 24 - Discrete Structure II

Intersection of Sets: Let A ={ 1, 2, 4} and B ={3, 4, 5, 6} the intersection of set A with the set B is the set
that consists of all elements in A and in B. We denote the intersection of A and B by A ∩ B .

A ∩ B = { 4 }

Exercise
Let A = { a, b , c , d } and B = { c, d , e , f} find:

1. A ∪ B
2. A ∩ B

Answer:

1. A ∪ B = { a, b, c, d, e, f}
2. A ∩ B = { c, d}

Sets Difference

Definition
Let A and B be two sets, the set difference of A and B denoted by A – B, is the set of elements that
belong to A and not in B.

Let A = { a, b , c , d } and B = { c, d , e , f} find:
1. A – B
2. B – A

Answer:

1. A – B = { a, b}
2. B – A = { e, f}

Relations – Union – Intersection – Difference

Example

Let A ={ 1, 2, 3} and B ={1, 2, 3, 4}. Let R1 = { (1, 1), (2, 2), (3, 3)} and R2 = { (1, 1), (1, 2), (1, 3), (1, 4)}

Find

1. R1 ∪ R2
2. R1 ∩ R2
3. R1 - R2
4. R2 - R1

Solution

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