Sets-Quiz-11

Sets Quiz-11

Dear Readers,

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. In a set of ants in a locality, two ants are said to be related iff they walk on a same straight line, then the relation is

•  Reflexive and symmetric
•  Symmetric and transitive
•  Reflexive and transitive
•  Equivalence

Solution

Q2.If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets A×B and B×A are

•  2⁹⁹
•  99²
•  100
•  18

Solution

Q3.  If A={x,y}, then the power set of A is

•  {x^y,y^x}
•  {ϕ,x,y}
•  {ϕ,{x},{2y}}
•  {ϕ,{x},{y},{x,y}}

Solution

Q4. On the set of human beings a relation R is defined as follows: "aRb iff a and b have the same brother”. Then R is

•  Only reflexive
•  Only symmetric
•  Only transitive
•  Equivalence

Solution

Q5.The relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)} on set A={1,2,3} is

•  Reflexive but not symmetric
•  Reflexive but not transitive
•  Symmetric and transitive
•  Neither symmetric nor transitive

Solution

Q6.Consider the following statements: p∶ Every reflexive relation is symmetric relation q∶ Every anti-symmetric relation is reflexive Which of the following is/are true?

•  p alone
•  q alone
• Both p and q
•  Neither p nor q

Solution

Q7.

•  A∩B
•  A∪B
•  B-A
•  (A-B)∪( B-A)

Solution

Q8.Let n(U)=700,n(A)=200,n(B)=300 and n(A∩B)=100. Then, n(A^c∩B^c)=

•  400
•  600
•  300
•  200

Solution

Q9.Which of the following is an equivalence relation?

•  Is father of
•  Is less than
•  Is congruent to
•  Is an uncle of

Solution
c) Is congruent to

Q10. In order that a relation R defined on a non-empty set A is an equivalence relation, it is sufficient, if R

•  Is reflective
•  Is symmetric
•  Is transitive
• Possesses all the above three properties

Solution
d) Is transitive