Discrete Maths - Sets

116. If n > 2, then number of surjections that can be defined from {1, 2, 3, ...n} onto (1, 2) is

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117. Consider the following relations :
R1 (a, b) iff (a + b) is even over the set of integers
R2 (a, b) iff (a + b) is odd over the set of integers.
R3 (a, b) ifa.b > 0 over the set of non zero rational numbers.
R4 (a, b) if I a - b I  < = 2 over the set of natural numbers. 
Which of the following statements is correct ?

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118. A relation on the integers 0 through 4 is defined by :
R = {(x, y) : x + y ≤ 2x).

Which of the properties listed below applies to this relation?
I.  Transitivity
II. Symmetry
III. Relexivity

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119. Let R1 and R2 be two equivalence relations on a set. Consider following assertions : 
I.  R1 ∪ R2 is an equivalence relation.
II. R1 ∩ R2 is an equivalence relation.
Which of the following is correct ?

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120. A relation over the set S = {x, y, z} is defined by :
{(x, x), (x, y), (y, x), (x, z), (y, z), (y, y), (z, z)}.
What properties hold for this relation?

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Related Quiz.
Sets