CBSE Questions for Class 11 Commerce Applied Mathematics Set Theory Quiz 1 - MCQExams.com

Examine the following statements: 
$$\left \{    a, b  \right \} \subset $$ { b, a,  c]
  • True
  • False
If $$X$$ and $$Y$$ are any two non empty sets then what is $$\displaystyle \left ( X-Y \right )'$$ equal to?
  • $$X' - Y'$$
  • $$\displaystyle {X}'\cap Y $$
  • $$\displaystyle {X}'\cup Y $$
  • $$X - Y'$$
If $$A$$ and $$B$$ are non empty sets and A' and B' represents their compliments respectively then
  • $$A - B = A' - B'$$
  • $$A - A' = B - B'$$
  • $$A - B = B' - A'$$
  • $$A - B' = A' - B$$
If $$\displaystyle \xi =\left \{ 2,3,4,5,6,7,8,9,10,11 \right \}$$
$$\displaystyle A =\left \{ 3,5,7,9,11 \right \}$$
$$\displaystyle B =\left \{ 7,8,9,10,11 \right \}$$, then find $$(A - B)'$$
  • $$(A - B)' = \{2,4,6,7,8,9,10,11\}$$
  • $$(A - B)' = \{2,4,6,7,8,9,11\}$$
  • $$(A - B)' = \{2,4,6,7,9,10,11\}$$
  • $$(A - B)' = \{2,4,6,8,9,10,11\}$$
State True or False
$$\displaystyle A\cup A'=\phi $$
  • True
  • False
The set of all those elements of A and B which are common to both is called
  • union of two sets
  • intersection of two sets
  • disjoint sets
  • none of these
Given $$K=\left \{B, A, N, T, I\right \}$$. Then the number of subsets of K, that contain both A, N is
  • 8
  • 16
  • 24
  • 32
In an examination $$70\%$$ students passed both in Mathematics and Physics $$85\%$$ passed in Mathematics and $$80\%$$ passed in Physics If $$30$$ students have failed in both the subjects then the total number of students who appeared in the examination is equal to : 
  • $$900$$
  • $$600$$
  • $$150$$
  • $$100$$
If $$n(A) = 65, n(B) = 32$$ and $$\displaystyle n\left ( A\cap B \right )=14 $$, then $$\displaystyle n\left ( A\Delta  B \right ) $$ equals
  • $$65$$
  • $$47$$
  • $$97$$
  • $$69$$
If $$n(A) = 115$$, $$n(B) = 326$$, $$n(A - B) = 47$$ then $$\displaystyle n\left ( A\cup B \right )$$ is equal to
  • $$373$$
  • $$165$$
  • $$370$$
  • None
If P is true and Q is false, then Bi-implication of p and q is
  • True
  • False
For any two sets $$ A$$ and $$B, A = B$$ is equivalent to
  • $$A - B = B -A$$
  • $$A \cup B = A \cap B$$
  • $$A \cup C = B \cup C$$ and $$A \cap C = B \cap C $$ for any set $$C$$
  • $$A \cap B = \phi $$
set of irrational numbers is $$\displaystyle \left \{ \sqrt{8}, \pi  \right \}$$
  • True
  • False
set of rational numbers is 
$$\displaystyle \left \{ -6,-5\frac{3}{4}, -\sqrt{4}, -\frac{3}{5}, -\frac{3}{8}, 0, \frac{4}{5}, 1, 1\frac{2}{3}, 3.01, 8.47  \right \}$$
  • True
  • False
State true or false.
Given universal set= $$\displaystyle =\left \{ -6,-5\frac{3}{4}, -\sqrt{4}, -\frac{3}{5}, -\frac{3}{8}, 0, \frac{4}{5}, 1, 1\frac{2}{3}, \sqrt{8}, 3.01, \pi , 8.47  \right \}$$ 
From the given set, the set of integers is $$\displaystyle \left \{ -6,-\sqrt{4}, 0,1 \right \}$$.
  • True
  • False
Let $$A$$ $$=$$ set of all cuboids and B $$=$$ set of all cubes. Which of the following is true?
  • $$A\subset B$$
  • $$B\subset A$$
  • $$B=A$$
  • $$B\in A$$

Suppose $${ A }_{ 1 },{ A }_{ 2 },...,{ A }_{ 30 }$$ are thirty sets, each with five elements and $${ B }_{ 1 },{ B }_{ 2 },...,{ B }_{ 30 }$$ are $$n$$ sets ecah with three elements. Let $$\displaystyle \bigcup _{ i=1 }^{ 30 }{ { A }_{ i }= } \bigcup _{ j=1 }^{ n }{ { B }_{ j } } =S$$

If each element of $$S$$ belongs to exactly ten of the $${ A }_{ i }'s$$ and exactly none of the $${ B }_{ j }'s$$ then $$n=$$
  • 45
  • 35
  • 40
  • none of these
A $$\bigcup \phi = $$
  • $$\phi$$
  • 2
  • A
  • 0

Let $$n$$ be a fixed positive integer. Let a relation $$R$$ defined on $$I$$ (the set of all integers) as follows: $$aRb$$ iff $$n/(a-b)$$, that is, iff $$a-b$$ is divisible by $$n$$, then, the relation $$R$$ is
  • Reflexive only
  • Symmetric only
  • Transitive only
  • An equivalence relation
If X $$=$$ (multiples of 2), Y $$=$$ (multiples of 5), Z $$=$$ (multiples of 10), then $$X \cap  ( Y \cap  Z )$$ is equal to
  • multiples of 10
  • multiples of 5
  • multiples of 2
  • multiples of 7
In a locality two-thirds of the people have cable TV one-fifth have Dish TV and one-tenth have both What is the fraction of people having either cable TV or Dish TV?
274249_296d269d34fd4621b6d08326aa577e08.png
  • $$\displaystyle \frac{2}{3}$$
  • $$\dfrac13$$
  • $$\dfrac45$$
  • $$\dfrac35$$
Let $$P =$$ Set of all integral multiples of $$3 $$; $$Q =$$ Set of integral multiples of $$4 $$; $$R =$$ Set of all integral multiples of $$6$$. Consider the following relations :
$$1 $$ $$\displaystyle P\cup Q=R$$
$$2.$$ $$\displaystyle P\subset R$$
$$3.$$ $$\displaystyle R\subset \left ( P\cup Q \right )$$
Which of the relations given above is/are correct ?
  • only $$1$$
  • only $$2$$
  • only $$3$$
  • both $$2$$ and $$3$$
State true or false.
Given universal set= $$\displaystyle =\left \{ -6,-5\frac{3}{4}, -\sqrt{4}, -\frac{3}{5}, -\frac{3}{8}, 0, \frac{4}{5}, 1, 1\frac{2}{3}, \sqrt{8}, 3.01, \pi , 8.47  \right \}$$ 
From the given set, find set of non-negative integers is $$\displaystyle \left \{0,1  \right \}$$.
  • True
  • False
Given, universal set = {$$x \,\,\epsilon\,\, Z$$ : $$- 6 < x \leq 6$$}, N = {$$n$$ : $$n$$ is a non-negative number} and P = {$$x$$ : $$x$$ is a nonpositive number}. Find :$$P'$$
  • $$\{-1,-2,-3,-4,-5,-6\}$$ 
  •  $$\{1,2,3,4,5,6\}$$ 
  • $$\{0,1,2,3,4,5,6\}$$ 
  • $$\{0,-1,-2,-3,-4,-5,-6\}$$ 
If $$\displaystyle Q=\left\{ x:x=\frac { 1 }{ y } ,where\  \ y\ \in \ N \right\} $$, then find the correct one.
  • $$\displaystyle 0\quad \in \quad Q$$
  • $$\displaystyle 1\quad \in \quad Q$$
  • $$\displaystyle 2\quad \in \quad Q$$
  • $$\displaystyle \frac { 2 }{ 3 } \quad \in \quad Q$$
Which set is the subset of the set containing all the whole numbers?
  • $$\{1,2,3,4,.......\}$$
  • $$\{1\}$$
  • $$\{0\}$$
  • All of the above
Let $$A$$ is a finite set such that $$n(A)=6$$ then  $$n[P(A)]$$ is 
  • $$32$$
  • $$36$$
  • $$63$$
  • $$64$$
For any two sets A and B, if $$A\cup B=A\cap B\Leftrightarrow A=B$$
  • True
  • False
In Question some relationship have been expressed through symbols as defined below :     (N-83)
     + - x $$\displaystyle\div $$ = > <
     V $$\displaystyle\Lambda $$ ( ) U $$\displaystyle\cap $$ 0
    In question only one of the five relationship is correct Find the correct one and encircle its serial number on the space provided against the question ______________.
  • 24 $$\displaystyle\cap $$ 3 ( 4 V 2 ) 8
  • 24 U 3 V 4 $$\displaystyle\Lambda $$ 2 ) 8
  • 24 ( 3 0 4 ) 2 V 8
  • 24 0 3 ( 4 $$\displaystyle\Lambda $$ 2 V 8
  • 24 $$\displaystyle\Lambda $$ 3 V 4 U 2 ( 8
Set $$A$$ has $$3$$ elements and set $$B$$ has $$6$$ elements. What can be the minimum number of elements in $$A\cup B$$?
  • $$6$$
  • $$3$$
  • $$9$$
  • $$18$$
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