Q5 of 76 Page 2

Write the following relations as the sets of ordered pairs:

A relation R from the set {2, 3, 4, 5, 6} to the set {1, 2, 3} defined by x = 2y.

Let A = {2, 3, 4, 5, 6} and B = {1, 2, 3}


Given, x = 2y where x {2, 3, 4, 5, 6} and y {1, 2, 3}


On putting y = 1, x = 2(1) = 2 A


On putting y = 2, x = 2(2) = 4 A


On putting y = 3, x = 2(3) = 6 A


∴ R = {(2, 1), (4, 2), (6, 3)}


More from this chapter

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3

Let A be the set of first five natural and let R be a relation on A defined as follows: (x, y) R x ≤ y

Express R and R-1 as sets of ordered pairs. Determine also


i. the domain of R‑1


ii. The Range of R.

 4

Find the inverse relation R-1 in each of the following cases:

i. R= {(1, 2), (1, 3), (2, 3), (3, 2), (5, 6)}


ii. R= {(x, y) : x, y N; x + 2y = 8}


iii. R is a relation from {11, 12, 13} to (8, 10, 12} defined by y = x – 3

 5

Write the following relations as the sets of ordered pairs:

A relation R on the set {1,2,3,4,5,6,7} defined by


(x, y) R x is relatively prime to y.

 5

Write the following relations as the sets of ordered pairs:

A relation R on the set {0,1,2,…,10} defined by


2x + 3y = 12.