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71. The identity element in the group

with respect to matrix multiplication is

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72. A subset H of a group (G,*) is a group if

a,b ∈ H=> a * b ∈ H

a ∈ H => a^{-1 }∈ H

a,b ∈ H=> a * b^{-1} ∈ H

H contains the identity element

73. If A = {1, 2, 3} then relation S = {(1, 1), (2, 2)} is

symmetric only

anti-symmetric only

both symmetric and anti-symmetric

an equivalence relation

74. Which of the following statements is true?

Every equivalence relation is a partial-ordering relation.

Number of relations form A = {x, y, z} to B= (1, 2), is 64.

Empty relation φis reflexive

Properties of a relation being symmetric and being un-symmetric are negative of each other.

75. Let A = {1, 2, .....3 }Define ~ by x ~ y ⇔ x divides y. Then ~ is

reflexive, but not a partial-ordering

symmetric

a partial-ordering relation

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