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# Set Theory and Algebra MCQ - Sets

46:

If R = {(1, 2),(2, 3),(3, 3)} be a relation defined on A= {1, 2, 3} then R . R( = R2) is

 A. R itself B. {(1, 2),(1, 3),(3, 3)} C. {(1, 3),(2, 3),(3, 3)} D. {(2, 1),(1, 3),(2, 3)} Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
47:

A subset H of a group(G,*) is a group if

 A. a,b ∈ H  ⇒ a * b ∈ H B. a ∈ H⇒ a-1 ∈ H C. a,b ∈ H  ⇒ a * b-1 ∈ H D. H contains the identity element Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
48:

If A = {1, 2, 3} then relation S = {(1, 1), (2, 2)} is

 A. symmetric only B. anti-symmetric only C. both symmetric and anti-symmetric D. an equivalence relation Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
49:

Which of the following statements is true?

 A. Every equivalence relation is a partial-ordering relation. B. Number of relations form A = {x, y, z} to B= {1, 2} is 64. C. Empty relation  φ is reflexive D. Properties of a relation being symmetric and being ant-symmetric are negative of each other. Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here:
50:

Let A = {1, 2, .....3 }
Define ~ by x ~ y  ⇔ x divides y. Then ~ is

 A. relexive, but not a partial-ordering B. symmetric C. an equivalence relation D. a partial-ordering relation Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here:

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