Question

Which of the following relations are Symmetric?
(a) ‘is a sister’ on the set of all members of a family.
(b) ‘is a multiple of’ on the set of N.
(c) ‘is a divisor of’ on the set of Integers.
(d) ‘is perpendicular to’ on the set of lines on a plane

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Which of the following relations are Symmetric

(a) ‘is a sister’ on the set of all members of a family.

(b) ‘is a multiple of’ on the set of N.

(c) ‘is a divisor of’ on the set of Integers.

(d) ‘is perpendicular to’ on the set of lines on a plane

CONCEPT TO BE IMPLEMENTED

A relation R is said to be symmetric if (a, b) ∈ R and (b, c) ∈ R

EVALUATION

CHECKING FOR OPTION : (a)

‘is a sister’ on the set of all members of a family.

NO this relation is not symmetric.

As if A is a sister of B then B is not sister of A

CHECKING FOR OPTION : (b)

‘is a multiple of’ on the set of N.

NO this relation is not symmetric.

Since 4 is a multiple of 2 but 2 is not a multiple of 4

CHECKING FOR OPTION : (c)

‘is a divisor of’ on the set of Integers.

NO this relation is not symmetric.

Since 3 is a divisor of 6 but 6 is not a divisor of 3

CHECKING FOR OPTION : (d)

‘is perpendicular to’ on the set of lines on a plane

Yes this relation is symmetric.

Since if a line L₁ is perpendicular to L₂ then the line L₂ is perpendicular to L₁

FINAL ANSWER

Hence the correct option is

(d) ‘is perpendicular to’ on the set of lines on a plane

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