CBSE Questions for Class 11 Commerce Applied Mathematics Set Theory Quiz 2 - MCQExams.com

If $$S$$ and $$T$$ are two sets such that $$S$$ has $$21$$ elements, $$T$$ has $$32$$ elements and $$\displaystyle S\cap T$$ has $$11$$ elements, then
find the number of elements in $$\displaystyle S\cup  T$$.
  • $$47$$
  • $$42$$
  • $$37$$
  • $$52$$
In a community of $$  175$$ persons, $$40$$ read TOI, $$50$$ read the Samachar Patrika and $$100$$ do not read either. How many persons read both the papers?
  • $$16$$
  • $$17$$
  • $$15$$
  • $$14$$
Let  $$U=\{x: \in, W: 3<x< 12\} $$, $$B=\{4,6,8,10\}$$ . $$B'$$
  • $$\{6,7,9,11,12\}$$
  • $$\{5,7,9,11\}$$
  • $$\{5,7,9,10,11,12 \}$$
  • None of the above
M represents the children in a class who have no brothers and 8 represents the children who have no sisters. $$+$$ denotes union, $$*$$ denotes intersection, and $$(^\prime)$$ denotes complement. The set of children who have no siblings is
  • $$S^\prime+M^\prime$$
  • $$(S*M)^\prime$$
  • $$(S+M)^\prime$$
  • $$S*M$$
Which of the following has only one subset?
  • $$\{0,1\}$$
  • $$\{1\}$$
  • $$\{0\}$$
  • $$\{\}$$
$$(A\cup B)'$$
  • $$\left \{1,2,3,4,5,6\right \}$$
  • $$\left \{7,8\right \}$$
  • $$\left \{3,4,5\right \}$$
  • none
$$P\cap Q\cup R$$
  • $$\left \{b, c, d, h, i, j\right \}$$
  • $$\left \{b, c, d, g, i, j\right \}$$
  • $$\left \{b, c, f, h, i, j\right \}$$
  • $$\left \{b, c, f, g, i, j\right \}$$
State whether following statement is true or false.
Given $$\mu = \left \{x / x \text {is an integer}, -4\leq x \leq 6\right \}$$,
$$P' = \left \{-4, -3, 0, 1, 2, 4, 6\right \}$$
$$Q' = \left \{-3, -2, 1, 3, 6\right \}$$
The elements of the set $$P$$ are $$P = \left \{-2, -1, 3, 5\right \}$$.
  • True
  • False
If $$A, B$$ and $$C$$ are any three set, then $$A \cup (B\cap C) =$$
  • $$ (A \cup B) \cup (A\cup C)$$
  • $$ (A \cup B) \cap (A\cup C)$$
  • $$ (A \cap B) \cap (A\cap C)$$
  • none
The set $$\displaystyle A=\left\{ x:x\in { x }^{ 2 }=16\quad and\quad 2x=6 \right\} $$ equals:
  • Null set
  • Singleton set
  • Infinite set
  • Not a Well Defined Collection
$$(P\cap Q)\cup (Q\cap R)$$
  • $$\left \{b, c, f\right \}$$
  • $$\left \{b, c, d\right \}$$
  • $$\left \{b, c, d, f\right \}$$
  • $$\left \{b, c, f, g\right \}$$
Let $$A$$ and $$B$$ be two sets such that $$A\cap B=\phi$$. Find the value of $$(A\cup B')=$$
  • $$A'$$
  • $$B$$
  • $$\phi$$
  • none of these
In a school with an envolment of $$950$$ students, each student must join either the lions club or the country club or both. Given that $$646$$ students are members of the lions club and $$532$$ are members of the country club, calculate the number of students who are members of both clubs
  • $$228$$
  • $$230$$
  • $$232$$
  • $$234$$
A survey was carried out to find out the types of shampoo that a group of $$150$$ women have tried. It was found that $$84$$ women have used brand A shampoo, $$93$$ have used brand B, and $$69$$ have used brand C of these women, $$45$$ have tried brands A and B, $$25$$ have tried brands A and C and $$40$$ have tried brand B and C. Determine the number of women who have tried (a) all three brands, (b) only brand A
  • (a) $$14$$ (b) $$28$$
  • (a) $$15$$ (b) $$28$$
  • (a) $$14$$ (b) $$29$$
  • (a) $$16$$ (b) $$29$$
If $$A = \left \{1, 2, 3, 4\right \}$$, what is the number of subsets of A with at least three elements?
  • $$3$$
  • $$4$$
  • $$5$$
  • $$10$$
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
  • $$A\cap B = \oslash$$
The set of integers is closed with respect to which one of the following?
  • Addition only
  • Multiplication only
  • By addition and multiplication
  • Division
In the Venn diagram, the numbers represent the number of elements in the subsets. Given that $$\xi = F\cup G\cup H$$ and $$n(\xi) = 42$$, find $$n(G'\cup H)$$
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  • $$18$$
  • $$28$$
  • $$30$$
  • $$38$$
If A and B be two sets containing $$4$$ and $$8$$ elements respectively, what can be the maximum number of elements in $$A\cup B$$? Find also, the minimum number of elements in $$(A\cup B)$$?
  • Maximum number of elements $$= 12$$
    Minimum number of elements $$= 8$$
  • Maximum number of elements $$= 14$$
    Minimum number of elements $$= 8$$
  • Maximum number of elements $$= 12$$
    Minimum number of elements $$= 9$$
  • Maximum number of elements $$= 14$$
    Minimum number of elements $$= 7$$
How many of these students are taking physics?
  • $$n(P) = 45$$
  • $$n(P) = 40$$
  • $$n(P) = 50$$
  • $$n(P) = 55$$
Which one of the following is incorrect?
  • Every subset of a finite set is finite
  • $$P=\left \{ x:x-8=-8 \right \}$$ is a singleton set
  • Every set has a proper set
  • Every non-empty set has at least two subsets, $$\phi$$ and the set itself
The number of elements of the set $$\left \{ x:x\in Z,x^{2}=1 \right \}$$ is :
  • $$3$$
  • $$2$$
  • $$1$$
  • $$0$$
State whether the following statement is True or False
If $$U=\left\{1,2,3,4,5,6,7\right\}$$ and $$A=\left\{5,6,7\right\}$$, then $$U$$ is the subset of $$A$$.
  • True
  • False
Let $$n(A)=28$$,$$n(A\cap B)=8$$, $$n(A\cup B)=52$$, then $$n(A\cap B')=$$.
  • $$30$$
  • $$32$$
  • $$20$$
  • none of these
From among the given alternatives select the one in which the set of numbers is most like the set of numbers given in the question.
Given set $$:$$ $$(7, 15, 31)$$
  • $$7, 13, 28$$
  • $$5, 13, 28$$
  • $$9, 13, 26$$
  • $$5, 13, 29$$
If $$A \subset B$$, then $$A \cap B$$ is
  • $$B$$
  • $$A\setminus B$$
  • $$A$$
  • $$B \setminus A$$
Upper limit of class $$'41 - 50'$$ is __________.
  • $$41$$
  • $$50$$
  • $$45$$
  • $$91$$
Let $$A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$$. Then the number of subsets of $$A$$ containing exactly two elements is
  • $$20$$
  • $$40$$
  • $$45$$
  • $$90$$
State the following statement is True or False.
If we have two sets, $$A$$ and $$B$$ and every element of the set $$A$$ is also the element of the set $$B$$. then we can say $$A$$ is subset of the set $$B$$.
  • True
  • False
In a class of $$60$$ students, $$45$$ students like music, $$50$$ students like dancing, $$5$$ students like neither. Then the number of students in the class who like both music and dancing is
  • $$35$$
  • $$40$$
  • $$50$$
  • $$55$$
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