show that the relation R on R defined as R={(a,b);a<b2} is neither reflexive nor symmetric nor transitive
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Answer:
R = {(a, b): a ≤ b2}
It can be observed that
(12,12)∉R,since12>(12)2=14
∴R is not reflexive.
Now, (1, 4) ∈ R as 1 < 42
But, 4 is not less than 12.
∴(4, 1) ∉ R
∴R is not symmetric.
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.
Hence, R is neither reflexive, nor symmetric, nor transitive.
hope this helps you out
thank u
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