Q. How many elements are there in the smallest equivalence relation on a set with 8 elements?

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Q. The rank of smallest equivalence relation on a set with 12 distinct elements is _______

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Q. If a set A has 8 elements and a set B has 10 elements, how many relations are there from A to B?

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Q. Synonym for binary relation is _______

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Q. R is a binary relation on a set S and R is reflexive if and only if _______

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Q. If R₁ and R₂ are binary relations from set A to set B, then the equality ______ holds.

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Q. The condition for a binary relation to be symmetric is _______

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Q. ______ number of reflexive closure exists in a relation R = {(0,1), (1,1), (1,3), (2,1), (2,2), (3,0)} where {0, 1, 2, 3} ∈ A.

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Q. The transitive closure of the relation {(0,1), (1,2), (2,2), (3,4), (5,3), (5,4)} on the set {1, 2, 3, 4, 5} is _______

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Q. Amongst the properties {reflexivity, symmetry, antisymmetry, transitivity} the relation R={(a,b) ∈ N² | a!= b} satisfies _______ property.

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Q. The number of equivalence relations of the set {3, 6, 9, 12, 18} is ______

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Q. Let R₁ and R₂ be two equivalence relations on a set. Is R₁ ∪ R₂ an equivalence relation?

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Q. A relation R is defined on the set of integers as aRb if and only if a+b is even and R is termed as ______

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Q. The binary relation U = Φ (empty set) on a set A = {11, 23, 35} is _____

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Q. The binary relation {(1,1), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2)} on the set {1, 2, 3} is __________

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Q. Consider the relation: R’ (x, y) if and only if x, y>0 over the set of non-zero rational numbers,then R’ is _________

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Q. Let S be a set of n>0 elements. Let be the number Bᵣ of binary relations on S and let Bf be the number of functions from S to S. The expression for Bᵣ and Bf, in terms of n should be ____________

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Q. Let A be a set of k (k>0) elements. Which is larger between the number of binary relations (say, Nr) on A and the number of functions (say, Nf) from A to A?

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Q. Consider the binary relation, A = {(a,b) | b = a – 1 and a, b belong to {1, 2, 3}}. The reflexive transitive closure of A is?

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Q. Let R₁ be a relation from A = {1, 3, 5, 7} to B = {2, 4, 6, 8} and R₂ be another relation from B to C = {1, 2, 3, 4} as defined below:

i. An element a in A is related to an element b in B (under R₁) if a * b is divisible by 3.

ii. An element a in B is related to an element b in C (under R₂) if a * b is even but not divisible by 3. Which is the composite relation R₁R₂ from A to C?

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