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1 mark questions:

1. Show that the relation R in the set R of real numbers, defined as R = {(a, b): a ≤ b²} is  not   transitive.

Ans. R = {(a, b): a ≤ b²} 

Now,

(3, 2), (2, 1.5) ∈ R

(as 3 < 2² = 4 and 2 < (1.5)² = 2.25)

But, 3 > (1.5)² = 2.25

∴(3, 1.5) ∉ R

∴ R is not transitive.

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