Page 23 - Discrete Structure II

R1 = {(a, a), (a, b), (b, a), (b, b), (c, d), (d, a), (d, d)}

(a, a) and (a, b) -----------(a, b)

(a, b) and (b, a) ----------(a, a)

(a, b) and (b, b) ---------(a, b)

(b, a) and (a, a)----------(b, a)
(b, a) and (a, b) -------( b, b)

(b, b) and (b, a)------ (b, a)

(c, d) and (d, a)-------(c, a)

(c,d) and (d, d)

(d, a) and (a, a)
(d, a) and (a, b)

(d, d) and (d, a)

It is not transitive , because (c, d) and (d, a)-------(c, a) does not belong to R1

Combining Relations

Review
Union of Sets: Let A ={ 1, 2, 4} and B ={3, 4, 5, 6} the union of set A with the set B is the set consists of all
elements in A or in B. We denote the union of A and B by A ∪ B .

A ∪ B = { 1, 2, 3, 4, 5, 6}

Note: Any common element is listed just once.

Exercise:

Let A ={ 1, 2, 4, 8, 9} and B ={3, 4, 5, 6}
What is A ∪ B?

Answer: A ∪ B = { 1, 2, 3, 4, 5, 6, 8, 9} A ∪ B ={ 1, 2, 4, 8, 9, 3, 5, 6}

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