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66. 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

(74,40)

(32,40)

(23,11)

(7,11)

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67. If A = (1, 2, 3, 4). Let ~= {(1, 2), (1, 3), (4, 2)}. Then ~ is

not anti-symmetric

transitive

reflexive

symmetric

68. Which of the following statements is false ?

If R is reflexive, then R ∩ R^{-1} ≠ φ

R ∩ R^{-1} ≠ φ =>R is anti-symmetric.

If R, R' are equivalence relations in a set A, then R ∩ R' is also an equivalence relation in A.

If R, R' are reflexive relations in A, then R - R' is reflexive

69. 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)}

70. If * is defined on R* as a * b = '

1

2

1/2

1/3

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