## Sets Quiz-16

Mathematics is an important subject in JEE ADVANCED and other engineering exams. In any engineering enterance exam, Mathematics carries weightage of 33% of questions. In mathematics a set is a collection of distinct elements. The elements that make up a set can be letters, numbers, points in space, lines, other geometrical shapes, variables, or even other sets. Two sets are equal if and only if they have precisely the same elements. With focused practice good marks can be fetched from this section. These questions are very important in achieving your success in JEE and Other Engineering Exams.

Q1. Given n(U)=20,n(A)=12,n(B)=9,n(A∩B)=4, where U is the universal set, A and B are subsets of U, then n[(A∪B)^c] equals to
•  10
•  9
•  11
•  3
Solution
Q2.Let R be a relation on a set A such that R=R-1, then R is
•  Reflexive
•  Symmetric
•  Transitive
•  None of these
Solution
Q3.  Let X={1,2,3,4,5} and Y={1,3,5,7,9}. Which of the following is/are not relations from X to Y?
•  R1={(x,y)|y=2+x,x∈X,y∈Y}
•  R2={(1,1),(2,1),(3,3),(4,3),(5,5)}
•  R3={(1,1),(1,3),(3,5),(3,7),(5,7)}
•  R4={(1,3),(2,5),(2,4),(7,9)}
Solution

Q4. Set builder form of the relation R={(-2,-7),(-1,-4),(0,-1),(1,2),(2,5)} is
•  {(a,b):b=2a-3;a,b,∈Z}
•  ((x,y):y=3x-1;x,y∈Z}
•  {(a,b):b=3a-1;a,b∈N}
•  {(u,Ï…):Ï…=3u-1;-2≤u<3 and u∈Z}
Solution
Q5.If A={a,b,c},B={b,c,d} and C={a,d,c}, then (A-B)×(B∩C) is equal to
•  {(a,c),(a,d)}
•  {(a,b),(c,d)}
•  {(c,a),(d,a)}
•  {(a,c),(a,d),(b,d)}
Solution
Q6.If a set has 13 elements and R is a reflexive relation on A with n elements, then
•  13≤n≤26
•  0≤n≤26
• 13≤n≤169
•  0≤n≤169
Solution
Q7.If P is the set of all parallelograms, and T is the set of all trapeziums, then P∩T is
•  P
•  T
•  Ï•
•  None of these
Solution
Q8.If R={(a,b):a+b=4} is a relation on N, then R is
•  Reflexive
•  Symmetric
•  Antisymmetric
•  Transitive
Solution
Q9.X is the set of all residents in a colony and R is a relation defined on X as follows: “Two persons are related iff they speak the same language” The relation R is
•  Only symmetric
•  Only reflexive
•  Both symmetric and reflexive but not transitive
•  Equivalence
Solution
Q10. If A={4,6,10,12} and R is a relation defined on A as “two elements are related iff they have exactly one common factor other than 1”. Then the relation R is
•  Antisymmetric
•  Only transitive
•  Only symmetric
• Equivalence
Solution

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