Operations on Relations MCQ Quiz in বাংলা - Objective Question with Answer for Operations on Relations - বিনামূল্যে ডাউনলোড করুন [PDF]

Given,

P(n) = n² + n is odd      ---(1)

P(n) = P(n + 1) ∀n

P(1) = not true

P(n) = n(n + 1)

Thus ,P(n) is a product of two consecutive numbers & one of them must be odd & other will be even & the product of one odd & one even number will always results in even number, thus P(n) will always be even 

Thus P(n) is false for all n ∈ N

Concept:

If A, B and C are three sets such that  \(R\subseteq A\times B\) and \(S\subseteq B\times C\) then (SOR)^-1 = R^-1 O S^-1. It is clear that if a R b, b S c ⇒ a SOR c.

Calculation:

We know that  (ROR)-1 = R-1OR-1

Domain(R) = {1, 2, 7, 9} and Range(R) = {2, 3, 5, 7}

we see that,

1 → 2 → 3 ⇒ (1, 3) ∈ ROR

1 → 2 → 5 ⇒ (1, 5) ∈ ROR

9 → 7 → 3 ⇒ (9, 3) ∈ ROR

Hence ROR = {(1, 3), (1, 5), (9, 3)}

(ROR)-1 = {(3, 1), (5, 1), (3, 9)}

 R-1OR-1 = {(3, 1), (5, 1), (3, 9)}