Set Theory and Algebra MCQ - Sets

41:

Let (Z, *) be an algebraic structure, where Z is the set of integers and the operation * is defined by n * m = maximum (n, m). Which of the following statements is TRUE for (Z, *) ?

 A. (Z, *) is a monoid B. (Z, *) is an abelian group C. (Z, *) is a group D. None of these Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here:
42:

Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G ?

 A. g = g-1 for every g ∈ G B. g = g2 for every g ∈ G C. (g o h) 2 = g2o h2 for every g,h ∈ G D. G is of finite order Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
43:

If the binary operation * is deined on a set of ordered pairs of real numbers as
(a, b) * (c, d) = (ad + bc, bd)
and is associative, then
(1, 2) * (3, 5) * (3, 4) equals

 A. (74,40) B. (32,40) C. (23,11) D. (7,11) Answer Report Discuss Option: A Explanation : Click on Discuss to view users comments. Write your comments here:
44:

If A = (1, 2, 3, 4). Let  ~ = ((1, 2), (1, 3), (4, 2). Then  ~ is

 A. not anti-symmetric B. transitive C. reflexive D. symmetric Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here:
45:

Which of the following statements is false ?

 A. If R is relexive, then R ∩ R-1≠ φ B. R ∩ R-1≠ φ =>R is anti-symmetric. C. If R, R' are equivalence relations in a set A, then R  ∩ R' is also an equivalence relation in A. D. If R, R' are reflexive relations in A, then R - R' is reflexive Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here: