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2. Relations
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Q19 of 76 Page 2

Figure 2.15 shows a relationship between the sets P and Q. Write this relation in

a. Set builder form


b. Roster form


c. What is its domain and range?


i. Since 5 – 3 = 6 – 4 = 7 – 5 = 2


∴ x – y = 2 where x P and y Q


So,


R = {(x, y): x – y = 2, x P, y Q}


ii. Now, R = {(5, 3), (6, 4), (7, 5)}


iii. Domain of relation R = {5, 6, 7}


Range of relation R = {3, 4, 5}


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17

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

18

Let A= {1, 2, 3, 4, 5, 6}. Let R be a relation on A defined by

R= {(a, b): a, b A, b is exactly divisible by a}


i. Write R in roster form


ii. Find the domain of R


iii. Find the range of R.

20

Let R be the relation on Z defined by R = {(a, b) Z, a – b is an integer}. Find the domain and range of R.

21

For the relation R1 defined on R by the rule (a, b) R1 1 + ab > 0. Prove that: (a, b) R1 and (b,c) R1 (a, c) R1 is not true for all a, b, c R.

Questions · 76
2. Relations
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