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Check Whether the Relation R In R Defined as R = {(A, B): A ≤ B3} is Reflexive, Symmetric Or Transitive. - CBSE (Commerce) Class 12 - Mathematics

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Question

Check whether the relation R on R defined as R = {(ab): a ≤ b3} is reflexive, symmetric or transitive.

Solution

R = {(ab): ≤ b3}

It is observed that `(1/2, 1/2) in R as 1/2 >(1/2)^3 = 1/8`

∴ R is not reflexive.

Now,

(1, 2) ∈ R (as 1 < 23 = 8)

But,

(2, 1) ∉ R (as 2 > 13 = 1)

∴ R is not symmetric.

We have `(3, 3/2), (3/2 , 6/5) in "R as "  3 < (3/2)^3 and 3/2 < (6/5)^3`

But  `(3, 6/5)  "∉" " R as " 3 > (6/5)^3`

`∴ R is not transitive.

Hence, R is neither reflexive, nor symmetric, nor transitive.

  Is there an error in this question or solution?
Solution Check Whether the Relation R In R Defined as R = {(A, B): A ≤ B3} is Reflexive, Symmetric Or Transitive. Concept: Types of Relations.
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