Operations on Relations MCQ Quiz in मराठी - Objective Question with Answer for Operations on Relations - मोफत PDF डाउनलोड करा

Last updated on Apr 20, 2025

पाईये Operations on Relations उत्तरे आणि तपशीलवार उपायांसह एकाधिक निवड प्रश्न (MCQ क्विझ). हे मोफत डाउनलोड करा Operations on Relations एमसीक्यू क्विझ पीडीएफ आणि बँकिंग, एसएससी, रेल्वे, यूपीएससी, स्टेट पीएससी यासारख्या तुमच्या आगामी परीक्षांची तयारी करा.

Latest Operations on Relations MCQ Objective Questions

Top Operations on Relations MCQ Objective Questions

Operations on Relations Question 1:

Let P(n)=n2 + n is odd, then P(n) = P(n + 1)∀n and P(1) is not true, then which of the following is true?

  1. P(n) is false for all n ∈ N.
  2. P(n) is true for all n.
  3. P(n) is true for all n ∈ Z.
  4. P(n) is true for all n ≥ N.

Answer (Detailed Solution Below)

Option 1 : P(n) is false for all n ∈ N.

Operations on Relations Question 1 Detailed Solution

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

Operations on Relations Question 2:

Let R be a relation such that R = {(1, 2), (9, 7), (2, 5), (2, 3), (7, 3)} then what will be R-1OR-1 

  1. {(3, 1), (5, 1) (3, 9), (7, 3)}
  2. {(3, 1), (5, 1), (7, 3)}
  3. {(3, 1), (5, 1) (3, 9)}
  4. {(3, 1), (3, 9), (7, 3)}

Answer (Detailed Solution Below)

Option 3 : {(3, 1), (5, 1) (3, 9)}

Operations on Relations Question 2 Detailed Solution

Concept:

If A, B and C are three sets such that   and  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)}

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