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46. If R = {(1, 2),(2, 3),(3, 3)} be a relation defined on A= {1, 2, 3} then R . R( = R2) is
R itself
{(1, 2),(1, 3),(3, 3)}
{(1, 3),(2, 3),(3, 3)}
{(2, 1),(1, 3),(2, 3)}
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47. 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
48. 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
49. 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 φ is reflexive
Properties of a relation being symmetric and being ant-symmetric are negative of each other.
50. 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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