Discrete Maths MCQ - Sets

101 Let A = {1, 2, 3, 4} and B = {0, 1, -1, 2} and several sets of ordered pairs be specified as :

I. {(1, 0), (2, 1), (3, -1), (4, 2)}

II. {(1, 0), (2, -1), (3, 2)}

III. {(4, 1), (3, 2), (2, 3), (1, 4)}

IV. {(2, 1), (3, 0), (1, - 1), (3, 1), (4, 2)}

V. {(2, 0), (1, -1), (3, 2) (4, 1)}

Which of the sets of ordered pairs are onto functions from A → B ?

A
II and III
B
III and IV
C
I and V
D
IV and V

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102 The power set of the set S = [3, {1, 4}, 5] is

A
{S, 3, 1, 4, {1, 3, 5}, {1, 4, 5} {3, 4}, Φ}
B
{S, 3, {1, 4,}, 5}
C
{S, {3}, {3, {1, 4}}, {3, 5}, Φ}
D
None of these

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In a language survey of students, it is found that 80
students know English, 60 know French, 50 know
German, 30 known English and French, 20 know
French and German, 15 know English and German
And 10 students know all three languages.

103 How many students known French and one but not both out of English and German?

A
135
B
30
C
10
D
40

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104 The number of distinct reflexive and symmetric relations that can be defined on a 3 element set is

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105 If I is set of positive integers and relation R is defined over the set I by xRy if xy' = yx, then R is

A
reflexive but neither symmetric nor transitive
B
reflexive and transitive but not symmetric
C
reflexive and symmetric but not transitive
D
reflexive, symmetric and transitive

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