## Sets Quiz-8

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 n(A)=4,n(B)=3,n(A×B×C)=240, then n(C) is equal to
•  288
•  1
•  12
•  2
Solution
Q2.If A is a non-empty set, then which of the following is false? p∶ Every reflexive relation is a symmetric relation q∶ Every antisymmetric relation is reflexive Which of the following is/are true?
•  p alone5
•  q alone
•  Both p and q
•  Neither p nor q
Solution
Q3.  Three sets A,B,Care such that A=B∩C and B=C∩A, then
•  A⊂B
•  A⊃B
•  A≡B
•  A⊂B'
Solution

Q4. Let P={(x,y)│x2+y2=1,x,y∈R}. Then, P is
•  Reflexive
•  Symmetric
•  Transitive
•  Antisymmetric
Solution
Q5.Suppose A1,A2,…,A30 are thirty sets, each having 5 elements and B1,B2,…,Bn are n sets each with 3 elements, let ⋃i=130Ai=⋃j=1nBj=S and each element of S belongs to exactly 10 of the Ai's and exactly 9 of the Bj's. Then, n is equal to
•  115
•  83
•  45
•  None of these
Solution
Q6.Let L denote the set of all straight lines in a plane. Let a relation R be defined by Î± R Î²⇔Î±⊥Î²,Î±,Î²∈L. Then R is
•  Reflexive
•  Symmetric
• Transitive
•  None of these
Solution
b) Symmetric

Q7.Let X be a family of sets and R be a relation on X defined by 'A is disjoint from B'. Then, R is
•  Reflexive
•  Symmetric
•  Antisymmetric
•  Transitive
Solution

Q8.If R be a relation < from A={1,2,3,4} to B={1,3,5} i.e.(a,b)∈R⇔a<b, then R o R-1 is
•  {(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)}
•  {(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)}
•  {(3,3),(3,5),(5,3),(5,5)}
•  {(3,3),(3,4),(4,5)}
Solution
Q9.Let R be a relation on the set N be defined by {(x,y)│x,y∈N,2 x+y=41}. Then, R is
•  Reflexive
•  Symmetric
•  Transitive
•  None of these
Solution
Q10. Let A be the set of all animals. A relation R is defined as "aRb iff a and b are in different zoological parks”. Then R is
•  Only reflexive
•  Only symmetric
•  Only transitive
• Equivalence
Solution

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