Ordered Pairs, Equivalence relation

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An ordered pair has a pair of elements which occur in a definite order.An ordered pair has a pair of elements which occur in a definite order.

Take two numbers 3 and 5. If they form a pair (3,5) and the order of the numbers cannot be changed, these numbers are said to form an ordered pair.

(3, 5) (5, 3)

If two ordered pairs (a, b) and (x, y) are equal, (a, b) = (x, y) then a = x,

b = y.

If (3, y) = (x, 4) find x and y.

Since the ordered pairs are equal, then the first element of first pair = the first element of the second pair x = 3, similarly y = 4.

Ans: x = 3, y = 4

Given (2x + 3, 2y + 4) = (x + 6, 3 + 4y), find x and y.

The first elements are equal ordered pairs are equal.

2x + 3 = x + 6 x = 3

Similarly, the second elements are equal.

2y + 4 = 3 + 3y y = 1

Ans: x = 3 , y = 1