Relation

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #1

The total number of relations from set `A={a,b,c}` to set `B={d,e}` is -- (a) `2^6`, (b) `2^8`, (c) `2^4`, (d) `2^15`

Question No: #2

The total number of relations on set `A = {1, 2, 3, 4}` is -- (a) `2^4`, (b) `2^8`, (c) `2^12`, (d) `2^16`

Question No: #3

A relation `\rho` defined on a set `A = {1, 2, 3}` by `\rho = {(1,2), (2,3), (3,1)}`. Then the relation `\rho` is -- (a) reflexive, (b) symmetric, (c) transitive, (d) none of these.

Question No: #4

Let `A = {8, 9, 10, 11}` and `B = {2, 3, 4, 5}` be two sets. A relation `\rho` is defined from set `A` to set `B` by `x\rhoy \implies x` is divisible by `y`. Find domain of relation `\rho`.

Question No: #5

`\mathbb{R}` is a set of all real numbers. If a relation `\rho` over set `\mathbb{R}` is defined such that `\rho = {(a,b) : a-b \lt 3, AA a,b \in \mathbb{R}}`, then the relation `\rho` is -- (a) transitive, (b) equivalence, (c) reflexive, (d) symmetric.

Question No: #6

`\mathbb{R}` is a set of all real numbers. If a relation `\rho` over set `\mathbb{R}` is defined such that `\rho = {(a,b) \in \mathbb{R} \times \mathbb{R} : ab \gt 0}`. Then relation `\rho` is -- (a) reflexive & symmetric, but not transitive, (b) symmetric & transitive, but not reflexive, (c) reflexive & transitive, but not symmetric, (d) equivalence relation.

Question No: #7

A relation `R` on the set `A = {1, 2, 3}` is defined by, `a R b \implies |a-b| \le 5`, then which of the following statement is wrong-
(a) `R = {(1, 1), (2, 2), (3, 3), (2, 1), (1, 2), (2, 3), (3, 2)}`, (b) `R^{-1} = R`, (c) domain of definition of `R` is `{1, 2, 3}`, (d) range of `R` is `{5}`
Ans: (d) range of `R` is `{5}`
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Question No: #8

A relation `R = {(x,y) : x \gt y}` defined on the set `A = {x : x \in N, 1 \le x \le 5}`. Express `R` as the set of ordered pair.
Ans: {(2,1), (3,1), (3,2), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3), (5,4)}
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Question No: #9

A relation `R` defined on the set `A = {2, 5, 7, 10}` by `x R y \iff x \equiv y (mod 5)`. Express `R` as a set of ordered pair.
Ans: R ={(2, 7), (7, 2), (5, 10), (10, 5), (2, 2), (5, 5), (7, 7) , (10, 10)}
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Question No: #10

For the relation `R={(a,b) : a+b \le 7` and `a=1, 2, 3, 4` and `b \in \mathbb{N}}`, find domain of definition of `R^{-1}`.
Ans: {1, 2, 3, 4, 5, 6}
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