Relation


Q11.

The less-than relation, \lt, on reals is
GateOverflow

Q12.

Let L be a set with a relation R which is transitive, anti-symmetric and reflexive and for any two elements a, b \in L, let the least upper bound lub (a, b) and the greatest lower bound glb (a, b) exist. Which of the following is/are true?
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Q13.

Let R be a non-empty relation on a collection of sets defined by _{A}R_ B if and only if A \cap B = \phi. Then, (pick the true statement)
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Q14.

Suppose A is a finite set with n elements. The number of elements in the largest equivalence relation of A is
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Q15.

The binary relation S = \phi (empty set) on set A = {1,2,3} is
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Q16.

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
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Q17.

A relation R is defined on the set of integers as xRy iff (x + y) is even. Which of the following statements is true?
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Q18.

Consider the binary relation R = {(x,y), (x,z), (z,x), (z,y)} on the set {x,y,z}. Which one of the following is TRUE?
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Q19.

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) iff a.b > 0 over the set of non-zero rational numbers R4(a,b) iff |a - b| <= 2 over the set of natural numbers Which of the following statements is correct?
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Q20.

Let R be a symmetric and transitive relation on a set A. Then
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