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Determine Whether Each of the Following Relations Are Reflexive, Symmetric and Transitive: Relation R in the Set A = {1, 2, 3, 4, 5, 6} as - Mathematics

Determine whether each of the following relations are reflexive, symmetric and transitive:

Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(xy): y is divisible by x}

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Solution

A = {1, 2, 3, 4, 5, 6}

R = {(xy): y is divisible by x}

We know that any number (x) is divisible by itself.

=> (xx) ∈R

∴R is reflexive.

Now,

(2, 4) ∈R [as 4 is divisible by 2]

But,

(4, 2) ∉ R. [as 2 is not divisible by 4]

∴R is not symmetric.

Let (xy), (yz) ∈ R. Then, y is divisible by x and z is divisible by y.

z is divisible by x.

⇒ (xz) ∈R

∴R is transitive.

Hence, R is reflexive and transitive but not symmetric.

  Is there an error in this question or solution?
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APPEARS IN

NCERT Class 12 Maths
Chapter 1 Relations and Functions
Q 1.3 | Page 5
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