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2. Relations and Functions
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Q18 of 22 Page 2

Let R be the relation on Z defined by a R b if and only if a – b is an even
integer. Find (i) R, (ii) domain R, (iii) range of R.


(i) R = {(a, b): a and b are even integers} ∪ {(c, d): c and d are odd integers}
(ii) Domain = Z
(iii) Range = Z

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16
Write the relation R, where R = {(x,x3) : x is a prime number less than 10} in roster form.

17
Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A into B.

19
Which of the following relations are functions? If it is a function,
determine its domain and range:
(i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}

(ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}

(iii) {(1, 3), (1, 5), (2, 5)}

20
Find the domain and range of the following real functions:
(i) f(x) = -lxl (ii) f(x) = .

Questions · 22
2. Relations and Functions
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