SETS-QUIZ-2

MATHEMATICS SETS QUIZ-2

Dear Readers,

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background. 

Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced. 

Q1. A,B and C are three non-empty sets. If A⊂B and B⊂C, then which of the following is true?

•  B-A=C-B
•  A∩B∩C=B
•  A∪B=B∩C
•  A∪B∪C=A

Solution
We have, A⊂B and B⊂C ∴A∪B=B and B∩C=B ⇒A∪B=B∩C

Q2.In a set of teachers of a school, two teachers are said to be related if they “teach the same subject”, then the relation is

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

Solution
Clearly, given relation is an equivalence relation

Q3.  Let R be a reflexive relation on a set A and I be the identity relation on A. Then

•  R⊂I
•  I⊂R
•  R=I
•  NONE OF THESE

Solution
No solution available

Q4. 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 alone
•  q alone
•  Both p and q
•  Neithr p nor q

Solution
If A={1,2,3}, then R={(1,1),(2,2),(3,3),(1,2)} is reflexive on A but it is not symmetric So, a reflexive relation need not be symmetric The relation ‘is less than’ on the set Z of integers is antisymmetric but it is not reflexive

Q5.Out of 800 boys in a school 224 played cricket, 240 played hockey and 336 played
    basketball. Of the total, 64 played both basketball and hockey; 80 played cricket and
    basketball and 40 played cricket and hockey; 24 played all the three games.
     The number of boys who did not play any game is

•  160
•  240
•  216
•  128

Solution

Q6. If A={a,b,c,l,m,n}, then the maximum number of elements in any relation on A is

•  12
•  16
•  32
•  36

Solution
Any relation on A is a subset of A×A which contains 36 elements. Hence, maximum number of elements in a relation on A can be 36

Q7.

•  A-B=ϕ
•  B-A=B
•  A∩B≠ϕ
•  A∩B=A

Solution
Clearly, A is the set of all points on a circle with centre at the origin and radius 2 and B is the set of all points on a circle with centre at the origin and radius 3. The two circles do not intersect. Therefore, A∩B=ϕ⇒B-A=B

Q8.If A={1,2,3,4}, then the number of subsets of A that contain the element 2 but not 3, is

• 16
•  4
•  8
•  24

Solution
Required number of subsets is equal to the number of subsets containing 2 and any number of elements from the remaining elements 1 and 4 So, required number of elements =2²=4

Q9.In a rehabilitation programme, a group of 50 families were assured new houses and
    compensation by the government. Number of families who got both is equal to the number
    of families who got neither of the two. The number of families who got new houses is 6
    greater than the number of families who got compensation. How many families got houses?

•  22
•  28
•  23
•  25

Solution

Q10. 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
Clearly, the relation is symmetric but it is neither reflexive nor transitive