# Set Theory and Algebra MCQ - Algebra

26:

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:
27:

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  φis reflexive D. Properties of a relation being symmetric and being  un-symmetric are negative of each other. Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here:
28:

Let A = {1, 2, .....3 }

Defineby x ~ y  ⇔ x divides y. Then ~ is

 A. reflexive, 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:
29:

G (e, a, b, c} is an abelian group with 'e' as identity element. The order of the other elements are

 A. 2,2,3 B. 3,3,3 C. 2,2,4 D. 2,3,4 Answer Report Discuss Option: A Explanation : Click on Discuss to view users comments. Write your comments here:
30:

If every element of a group G is its own inverse, then G is

 A. finite B. infinite C. cyclic D. abelian 133. Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here: