Relations
1 In the set a relation is defined by
Then, is
(A) Reflexive (B) Symmetric
(C) Transitive (D) None of these
2 If then the number of subsets of that contain the element 2 but not 3, is
(A) 16 (B) 4
(C) 8 (D) 24
3 If and then
(A) 49 (B) 50
(C) 11 (D) 10
4 Let be a relation defined on the set of squares on a chess board such that iff and share a common side. Then, which of the
following is false for
(A) Reflexive (B) Symmetric
(C) Transitive (D) All the above
5 Let be a relation on the set be defined by Then, is
(A) Reflexive (B) Symmetric
(C) Transitive (D) None of these
6 If be a relation from to then is
(A) (C)
(B) (D)
7 is the set of all residents in a colony and is a relation defined on as follows:“Two persons are related iff they speak the same
language”The relation is
(A) Only symmetric
(B) Only reflexive
(C) Both symmetric and reflexive but not transitive
(D) Equivalence
8 For real numbers x and y, we write xRy ⇔ is an irrational number. Then the relation R is
(A) Reflexive (B) Symmetric
(C) Transitive (D) None of these
9 Let and are at the same distance from the origin be a relation, then the equivalence class of is the set :
(A) (B)
(C) (D)
10 The relation is:
(A) Reflexive but not symmetric
(B) Transitive but not reflexive
(C) Symmetric but not transitive
(D) Neither symmetric not trasnsitive
11
12
13 If relation R: (a, b) R (c, d) is only if ad – bc is divisible by 5 (a, b, c, d Z) then R is
(A) Reflexive
(B) Symmetric, Reflexive but not Transitive
(C) Reflexive, Transitive but nor symmetric
(D) Equivalence relation
14 Let Then, is
(A) Reflexive (B) Symmetric
(C) Transitive (D) Antisymmetric
15 If a set has 13 elements and is a reflexive relation on with elements, then
(A) (B)
(C) (D)
16 If and is a relation defined on as “two elements are related iff they have exactly one common factor other than 1”.
Then the relation is
(A) Antisymmetric (B) Only transitive
(C) Only symmetric (D) Equivalence
17 Let R be a relation over the set N × N and it is defined by Then R is
(A) Reflexive only (B) Symmetric only
(C) Transitive only (D) An equivalence relation
18 Let and ' ' be an equivalence relation on , defined by , if and only if . Then the number of
ordered pairs which satisfy this equivalence relation with ordered pair is equal to :
(A) 5 (B) 6
(C) 8 (D) 7
19 Let A = {1, 3, 4, 6, 9} and B = {2, 4, 5, 8, 10}. Let R be a relation on such that . Then the
number of elements in the set R is
(A) 52 (B) 160 (C) 26 (D) 180
20 Let A = {2, 3, 6, 8, 9, 11} and B = {1, 4, 5, 10, 15} Let R be a relation on A B define by (a, b) R (c, d) if and only if 3ad – 7bc is an even
integer. Then the relation R is
(A) reflexive but not symmetric
(B) transitive but not symmetric
(C) reflexive and symmetric but not transitive
(D) an equivalence relation
21 If A = {1, 2, 3, 4} then find number of symmetric relation on A which is not reflexive is
(A) 960
(B) 970
(C) 980
(D) 980
