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