## Sets Quiz-9

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. If A,B and C are three sets such that A∩B=A∩Cand A∪B=A∪C, then
•  A=C
•  B=C
•  A∩B=Ï•
•  A=B
Solution
Q2.Let A={ONGC,BHEL,SAIL,GAIL,IOCL} and R be a relation defined as “two elements of A are related if they share exactly one letter”. The relation R is
•  Anti-symmetric
•  Only transitive
•  Only symmetric
•  Equivalence
Solution
Q3.  Let Z denote the set of integers, then {x∈Z:|x-3|<4}n{x∈Z:|x-4|<5}=
•  {-1,0,1,2,3,4}
•  {-1,0,1,2,3,4,5}
•  {0,1,2,3,4,5,6}
•  {-1,0,1,2,3,5,6,7,8,9}
Solution

Q4. Let A={p,q,r}. Which of the following is not an equivalence relation on A?
•  R1={(p,q),(q,r),(p,r),(p,p)}
•  R2={(r,q),(r,p),(r,r),(q,q)}
•  R3={(p,p),(q,q),(r,r).(p,q)}
•  None of these
Solution
d) None of these
Q5.An integer m is said to be related to another integer n if m is a multiple of n. Then, the relation is
•  Reflexive and symmetric
•  Reflexive and transitive
•  Symmetric and transitive
•  Equivalence relation
Solution
Q6.For any two sets A and B, A-(A-B) equals
•  A
•  A-B
• A∩B
•  AC∩BC
Solution

Q7.If A,B and C are three non-empty sets such that any two of them are disjoint, then (A∪B∪C)∩(A∩B∩C)=
•  A
•  B
•  C
•  Ï•
Solution

Q8.Which one of the following relations on R is an equivalence relation?
•  a R1 b⇔|a|=|b|
•  a R2 b⇔a≥b
•  a R3 b⇔a divides b
•  a R4 b⇔a<b
Solution
a) a R1 b⇔|a|=|b|
Q9.If A={1,2,3,4,5},B={2,4,6},C={3,4,6}, then (A∪B)∩C is
•  {3, 4, 6}
•  {1, 2, 3}
•  {1, 4, 3}
•  None of these
Solution
Q10. If A={1,2,3},B{3,4},C{4,5,6}. Then, A∪(B∩C) is
•  {1, 2}
•  {Ï•}
•  {4, 5}
• {1, 2, 3, 4}
Solution

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