QuizSagar
4 years ago Like 232906
Questions 823
Contests 7
Consider the Binary relation S={(x,y)|x=y+1} and x,y ∈ {0,1,2}. The reflexive transitive closure of S is
- {(x,y)|y>x} and x,y ∈ {0,1,2}
- {(x,y)| y ≥ x} and x,y ∈ {0,1,2}
- {(x,y)|y < x} and x,y ∈ {0,1,2}
- {(x,y)| y ≤ x} and x,y ∈ {0,1,2}
- {(x,y)| y ≤ x} and x,y ∈ {0,1,2}
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The number of equivalence relations on the set {1,2,3,4} is
- 15
- 16
- 24
- 4
- 15
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Let n is total number of elements the total no of equivalence relation usng Bell Tree.
For n=1: 1
For n=2: 1 2
For n=3: 2 3 5
For n=4: 5 7 10 15
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The number of equivalence relations on the set {1,2,3} is
- 1
- 4
- 5
- 15
- 5
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Let n is total number of elements the total no of equivalence relation usng Bell Tree.
For n=1: 1
For n=2: 1 2
For n=3: 2 3 5
For n=4: 5 7 10 15
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The number of functions from an m element set to an n element set is
- m+n
- mⁿ
- n^m
- m*n
- n^m
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Consider the function f(x)=2x mod 3 where f:{0,1,2,3}→{0,1,2,3}. The function f is ___
- Injective only
- Surjective only
- Bijective
- Neither Injective nor surjective
- Injective only
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function f(x) mod 2 can be mapped like
A B
0 → 0
1 → 2
2 → 1
3 → 0
4 → 2
In set A every element point to some single element of Set B but In set B element e in not pointed by any element is set B. Therefore It is Injective only
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Suppose X and Y are |X| and |Y| are their respective cardinalities. It is given that there are exactly 97 functions from X to Y. From this one can conclude that
- |X|=97, |Y|=1
- |X|=1, |Y|=97
- |X|=97, |Y|=97
- None of the above
- |X|=1, |Y|=97
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Suppose X and Y are |X| and |Y| are their respective cardinalities. It is given that there are exactly 8 functions from X to Y. From this one can conclude that
- |X|=2, |Y|=4
- |X|=4, |Y|=2
- |X|=1, |Y|=4
- |X|=3, |Y|=2
- option4
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Given there is exactly 97 function from Y to X
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Suppose A is a finite set with n elements. The number of elements in the Largest equivalence relation of A is
- n
- n^n
- 1
- n+1
- n^n
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The number of binary relations on a set with n elements is:
- n^n
- 2^n
- 2^(n^n)
- None of the above
- 2^(n^n)
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The binary relation R = {(1, 1)}, (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4) } on the set A = { 1, 2, 3, 4} is
- Reflexive, Symmetric and Transitive
- Neither reflexive nor irreflexive but Transitive
- Irreflexive, Symmetric and Transitive
- Irreflexive and Antisymmetric
- Neither reflexive nor irreflexive but Transitive
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