Let A = Z , the set of integers. Let R 1 = { ( m , n ) ∈ Z × Z : ( m + 4 n ) is divisible by 5 in Z } , Let R 2 = { ( m , n ) ∈ Z × Z : ( m + 9 n ) is divisibile by 5 in Z Which one of the following is correct?

R 1 is not a symmetric relation on Z

E M B I B E

Alpha Question Bank for Engineering: Mathematics>Chapter 2 - Set Theory and Relations>Exercise-1>Q 30

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IMPORTANT

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Consider the following:
$1 .$ If $R = \{(a, b) \in N \times N : a divides b in N\}$ then the relation $R$ is reflexive and symmetric but not transitive.
$2 .$ If $A = \{1, 2, 3, 4, 5, 6\}$ and $R = \{(S_{1}, S_{2}) : S_{1}, S_{2} are subsets of A, S_{1} ⊄ S_{2}\},$ then the relation $R$ is reflexive but not symmetric and not transitive.

Which of the statements is/are correct?

28.57% studentsanswered this correctly

Important Questions on Set Theory and Relations

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 2 - Set Theory and Relations>Exercise-1>Q 31

Let

R

be a relation over the set

N \times N

and it is defined by

(a, b) R (c, d) \Rightarrow a + d = b + c

. Then

R

is.

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Alpha Question Bank for Engineering: Mathematics>Chapter 2 - Set Theory and Relations>Exercise-1>Q 32

Let

L

be the set of all straight lines in the Euclidean plane. Two lines

l_{1}

and

l_{2}

are said to be related by the relation

R

if

l_{1}

is parallel to

l_{2}

. Then

R

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 2 - Set Theory and Relations>Exercise-1>Q 33

Let

R = {(x, y) : x, y \in A, x + y = 5}

where

A = {1, 2, 3, 4, 5}

then

R

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 2 - Set Theory and Relations>Exercise-1>Q 34

Let

S

be a set of all square matrices of order

2 .

If a relation

R

defined on set

S

such that

ARB \Rightarrow AB = O,

where

O

is zero square matirx of order

2,

then relation

R

is

(A, B \in S)

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Alpha Question Bank for Engineering: Mathematics>Chapter 2 - Set Theory and Relations>Exercise-2>Q 1

For real numbers

x

and

y

, we write

x R y \Rightarrow x - y + \sqrt{2}

is an irrational number. Then the relation

R

is-

EASY

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Alpha Question Bank for Engineering: Mathematics>Chapter 2 - Set Theory and Relations>Exercise-2>Q 2

Let $A = N \times N$ be the Cartesian product of $N$ and $N$ . Let $S = \{((m, n), (p, q)) \in A \times A : m + q = n + p\}$ .

Consider the following statements

$I .$ If $((m, n), (p, q)) \in S,$ and $((p, q), (r, s)) \in S$ then $((r, s), (m, n)) \in S$
$I I .$ There exists at least one element $((m, n), (p, q)) \in S$ such that $((p, q), (m, n)) \notin S$
Which of the statements given above is/are correct?