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116. If n > 2, then number of surjections that can be defined from {1, 2, 3, ...n} onto (1, 2) is
2n
nP2
2n-2
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117. Consider the following relations :R1 (a, b) iff (a + b) is even over the set of integersR2 (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 ?
R1 and R2 are equivalence relations, R3 and R4 are not
R1 and R3 are equivalence relations, R2 and R4 are not
R1 and R4 are equivalence relations, R2 and R3 are not
R1, R2, R3 and R4 are all equivalence relations
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. TransitivityII. SymmetryIII. Relexivity
I only
III only
I and III
II and III
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 ?
Both assertions are true
Assertion I is true but assertion II is not true
Assertion II is true but assertion I is not true
Neither I nor II is true
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?
Symmetric
Reflexive
Antisymmetric
Irrelexive
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