CBSE Questions for Class 11 Commerce Applied Mathematics Set Theory Quiz 3 - MCQExams.com

Let $$A_1, A_2$$ and $$A_3$$ be subsets of a set $$X$$. Which one of the following is correct?
  • $$A_1\cup{A_2}\cup{A_3}$$ is the largest subset of $$X$$ containing elements of each of $$A_1, A_2$$ and $$A_3$$
  • $$A_1\cup{A_2}\cup{A_3}$$ is the smallest subset of $$X$$ containing either $$A_1$$ or $$A_2\cup{A_3}$$ but not both
  • The smallest subset of $$X$$ containing $$A_1\cup{A_2}$$ and $$A_3$$ equals the smallest subset of $$X$$ containing both $$A_1$$ and $$A_2\cup{A_3}$$ only if $$A_2=A_3$$
  • None of these
Statements:
I. Some Politicians are social workers.
II. All Doctors are social workers.
Conclusions:
I. Some Doctors are Politicians.
II. Some social workers are Doctors as well as Politicians.
  • Both conclusion (I) and (II) follow
  • Only conclusion (II) follow
  • Neither conclusion (I) nor (II) follow
  • Only conclusion (I) follow
How many rural uneducated people are employed?
903151_4fe16b67d5564414ac2d90e0d49214e5.png
  • $$10$$
  • $$6$$
  • $$12$$
  • $$14$$
If $$A=\left\{ 2,4\left\{ 5,6 \right\} ,8 \right\} $$, then which one of the following statements is not correct?
  • $$\left\{ 5,6 \right\} \subseteq A$$
  • $$\left\{ 5,6 \right\} \in A$$
  • $$\left\{ 2,4,8 \right\} \subseteq A$$
  • $$2,4,8\in A\quad $$
For two sets $$A$$ and $$B$$, $$ A\cap \left( A\cup B \right)=$$
  • $$A$$
  • $$B$$
  • $$ \phi$$
  • $$None\ of\ these$$
If $$A=\left\{a,b,c\right\},B=\left\{c,d,e\right\},C\left\{a,d,f\right\},$$ then $$A\times \left( B\cup C \right)$$ is
  • $$\left\{(a,d),(a,e),(a,c)\right\}$$
  • $$\left\{(a,d),(b,d),(c,d)\right\}$$
  • $$\left\{(d,a),(d,b),(d,c)\right\}$$
  • $$none\ of\ these$$
$$A$$ and $$B$$ are two sets having $$3$$ and $$5$$ elements respectively and having $$2$$ elements in common. Then the number of elements in $$A\times B$$ is
  • $$6$$
  • $$36$$
  • $$15$$
  • $$None\ of\ these$$
Let $$A$$ and $$B$$ have $$3$$ and $$6$$ elements respectively. What can be the minimum number of elements in $$A\cup B$$?
  • $$3$$
  • $$6$$
  • $$9$$
  • $$18$$
$$25$$ people for applied for programme $$A$$, $$50$$ people for programme $$B$$, $$10$$ people for both. So number of employee applied only for $$A$$ is
  • $$15$$
  • $$20$$
  • $$35$$
  • $$40$$
State the whether given statement is true or false
If $$A$$ is any set, prove that: $$A\subseteq \phi \Leftrightarrow A=\phi $$.
  • True
  • False
If $$P(A) = 0.8 , P(B) = 0.5 $$ & $$P(B/A) =0.4 $$ find (i) $$P(A \cap B) $$ (ii) $$P(A/B)$$ (iii) $$P(A\cup B)$$.
  • $$i) 0.32, ii)0.64 , iii)0.98$$
  • $$i) 0.62, ii)0.34 , iii)0.88$$
  • $$i) 0.66, ii)0.32 , iii)0.98$$
  • none
If two sets $$A$$ and $$B$$ are having $$80$$ elements in common, then the number of element common to each of the sets $$A\times B$$ and $$B\times A$$ are
  • $${2}^{80}$$
  • $${80}^{2}$$
  • $$81$$
  • $$79$$
Given P(A)=$$0.5,$$P(B)=$$0.2$$ and P(AB)=0.1;find
  • $$P\left( {A \cup B} \right)$$
  • $$P\left( {\overline A \cap B} \right)$$
  • $$P\left( {A \cup \overline B} \right)$$
  • $$P\left( {\overline A \cap \overline B} \right)$$
If $$n(A)$$ denotes the number of elements in set A and if $$n(A)=4, n(B)=5$$ and $$n(A\cap B)=3$$ then $$n\left[ \left( A\times B \right) \cap \left( B\times A \right)  \right] =$$
  • $$8$$
  • $$9$$
  • $$10$$
  • $$11$$
If $$n(A \cup B)=8, n(A)=6, n(B)=4$$, then $$n(A\cap B)$$=
  • $$2$$
  • $$4$$
  • $$6$$
  • $$8$$
The set $$\left( {A \cap B'} \right)' \cup \left( {B \cap C} \right)$$ is equal to :
  • $$A' \cup B \cup C$$
  • $$A' \cup B$$
  • $$A' \cup C'$$
  • $$A' \cap B$$
If A and B are any two sets, then $$ A \cup B$$ is  equal to: 
  • $$(A-B) \cup (B-A) \cup (A \cap B)$$
  • $$ (A^0 \cap B^0)^0$$
  • $$(A-B) \cup (B-A)$$
  • $$A \cup (B-A)$$
Let $$A, B$$ are two sets such that $$n(A)=6, n(B)=8$$ then the maximum number of elements in $$n(A\cup B)$$ is _________
  • $$7$$
  • $$9$$
  • $$14$$
  • $$None$$
If $$A=\left\{2, 4, 6, 8, 10\right\}, B=\left\{1, 3, 5, 7, 9\right\}$$, then $$A-B$$ =____________
  • $$\left\{\right\}$$
  • $$\left\{2, 4, 6, 8, 10\right\}$$
  • $$\left\{1, 3, 5, 7, 9\right\}$$
  • $$None$$
If A and B are two sets such that $$n(A)=17, n(B)=23, n(A \cup B)=38$$, find $$n(A \cap B)$$.
  • 1
  • 2
  • 3
  • 4
Which of the following is set ?
  • The collection of months having names starting with J.
  • The collection of smart boys in your class.
  • The collection of most talented persons.
  • The collection of sand grains in a Earth.
If X and Y are two sets such that $$n(X)=45, n(X \cup Y)=76, n(X \cap Y)=12,$$ find $$n(Y)$$.
  • $$41$$
  • $$43$$
  • $$49$$
  • $$47$$
State whether the following statement is true or false. Give reason to support your answer.
A set can have infinitely many subsets.
  • True
  • False
The number of subsets of the set $$A=\{ { a }_{ 1 },{ a }_{ 2 },.........{ a }_{ n }\} $$ which contain even number of elements is
  • $${ 2 }^{ n-1 }$$
  • $${ 2 }^{ n }-1$$
  • $${ 2 }^{ n }-2$$
  • $${ 2 }^{ n }$$
Let $$S=\{2,4,6,8,......20\}$$. What is the maximum number of subsets does $$S$$ have ?
  • $$10$$
  • $$20$$
  • $$512$$
  • $$1024$$
State whether the following statements are true(T) or false(F).Justify your answer.
A collection of stamps is a set.
  • True
  • False
State whether the following statements are true(T) or false(F).Justify your answer.
A group of boys playing cricket is a set.
  • True
  • False
State whether the following statements are true(T) or false(F).Justify your answer.
A collection of some fruits is a set.
  • True
  • False
Which of the following collections is a set?
  • Collection of all tasty fruits
  • Collection of all good football players of your school
  • Collection of all months of a year
  • Collection of $$5$$ most intelligent students of your class.
Examine whether the following statements are true or false:
$$(1,2,3)\subset (1,3,5)$$
  • True
  • False
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers