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 |
Option: C Explanation : Click on Discuss to view users comments. |
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 |
Option: C Explanation : Click on Discuss to view users comments. |
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. |
Option: B Explanation : Click on Discuss to view users comments. |