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 = g^{2} for every g ∈ G |
C. | (g o h)^{ 2} = g^{2}o h^{2 }for every g,h ∈ G |
D. | G is of finite order |
Option: C Explanation : |
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) |
Option: A Explanation : |
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 |
Option: B Explanation : |
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 |
Option: D Explanation : |