Sets - Class 11 Commerce Maths - Extra Questions

In an examination, $$35$$ % students failed in Hindi, $$45$$ % students failed in English and $$20$$ % students failed in both the subjects. What is the percentage of students passing in both the subjects?  

P(fail in hindi) $$=P(A)=35$$ %

P(fail in english) $$=P(B)=45$$ %

P(fail in both) $$=P(A\cap B)=20$$ %

$$P(A\cup B)=P(A)+P(B)-P(A\cap B)\\ =35+45-20$$

$$=60$$ % of students failed in atleast one.

No. of students who passed in both 

$$=100-60=40$$ %

If $$X$$ and $$Y$$ are two sets such that $$n ( X ) = 17$$ , $$n ( Y ) = 23$$ $$n ( X \cup Y ) = 38$$ find $$n ( X \cap Y )$$

$$n ( X ) = 17$$

$$n ( Y ) = 23$$  

$$n ( X \cup Y ) =38$$

$$n ( X \cap Y )=n(X)+n(Y)-n ( X \cup Y )$$

$$n ( X \cap Y )=17+23-38=2$$

$$n ( X \cap Y )=2$$

Let $$O=$$ Set of odd natural numbers $$=\{1,3,5,7,9,...\}$$ and $$E=$$ Set of even natural numbers $$=\{2,4,6,8,10,........\}$$ . Then show that $$28\in E$$ .

$$0 =  \{1,3,5,7,9,.....\}$$

$$E = \{2,4,6,8,10 ,...... \}$$

It is clear from the definition of $$E$$ , $$28  \in  \,E\,$$

If $$A=\left\{1, 3, 9, 11, 13\right\}$$ and $$B=\left\{1, 9, 11\right\}$$ then find $$A\cup B$$ and $$A\cap B$$ .

Given,

  $$A=\left\{1, 3, 9, 11, 13\right\}$$ and $$B=\left\{1, 9, 11\right\}$$ .

Now,

$$A\cup B$$

$$=\{1,3,9,11,13\}$$ .

And 

$$A\cap B$$

$$=\{1,9,11\}$$ .

In a group of $$950$$ persons, $$750$$ can speak Hindi and $$460$$ can speak English. Find how many can speak both Hindi and English.

Let A and B denote the sets of persons who can speak Hindi and English respectively. 

Then $$n(A\cup B)=950,$$  

$$n(A)=750$$  

$$n(B)=460$$ .

$$n(A\cap B)=n(A)+n(B)-n(A\cup B)$$  

$$750+460-950=260$$ .

260 persons can speak both Hindi and English.

Let $$u=\{1, 2, 3, 4, 5, 6, 7, 8, 9\}, A=\{1, 2, 3, 4\}, B=\{2, 4, 6, 8\}$$ and $$C=\{3, 4, 5, 6\}$$ . Find B'.

$$u=\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$$

$$A=\{1, 2, 3, 4\}$$  

$$B=\{2, 4, 6, 8\}$$  

$$C=\{3, 4, 5, 6\}$$

$$B^{\prime}=u-B$$ =  $$\{1,2,3,4,5,6,7,8,9\}-\{2,4,6,8\}$$

= $$\{1, 3, 5, 7, 9\}$$ .

If $$A -B = \phi$$ then $$A \cup B$$ =............

Given,

$$A-B=\phi$$ .

Then 

$$A\cup B$$

$$=(A-B)\cup(A\cap B)\cup (B-A)$$

$$=(A\cup B)\cup (B-A)$$ [ Using (1)]

$$=B$$ .

Complete the following statements 
1.A∩B=B⟹B........AA∩B=B⟹B........A

1. $$A\bigcap { B } =B$$

It means that A is subset of B $$\left( A\subset B \right)$$

$$B\supset A$$ (B is a superset of A)

2. $$A\subset B$$

(Image 1)

$$n\left( A-B \right)$$

$$A-B=\phi \left( \because A\subset B \right)$$

$$n\left( A-B \right) =0$$

3. $$A\subset B$$

(Image 2)

$$A\bigcap { \left( A\bigcup { B }  \right)  } '$$

$$A\bigcup { B } =B\left( \because A\subset B \right)$$

$$A\bigcap { B' }$$

$$=\phi$$ (From the diagram)

4. $$A-B=\phi$$

(Image 3)

$$n\left( A\bigcup { B }  \right)$$

$$=A+B$$

$$n\left( A\bigcup { B }  \right) =n\left( A \right) +n\left( B \right)$$

Solve :- $$-12x>30,$$ when 
(i) $$x$$ is a natural number 
(ii) $$x$$ is an integer.

$$-12x>30$$

or, $$12x<-30$$

or, $$x<\cfrac { -5 }{ 2 }$$

i) When $$x\in \mathbb{N}\quad x=\phi$$

ii) When $$x\epsilon I\quad x\in \left[ -\infty ,-3 \right]$$

If $$A=\{1, 2\}$$ and $$B=\{1, 3\}$$ , find $$A\times B$$ and $$B\times A$$ .

If $$A=\{1, 2, 3\}$$ and $$B=\{2, 4\}$$ , what are $$A\times B, B\times A, A\times A, B\times B$$ , and $$(A\times B)\cap (B\times A)$$

Let $$A=\{1, 2, 3\}$$ and $$B=\{3, 4\}$$ . Find $$A\times B$$ and show it graphically.

If A and B are two sets having $$3$$ elements in common. If $$n(A)=5, n(B)=4$$ , find $$n(A\times B)$$ and $$n\{(A\times B)\cap (B\times A)\}$$ .

Class 11 Commerce Maths Extra Questions

• Binomial Theorem Extra Questions
• Complex Numbers And Quadratic Equations Extra Questions
• Conic Sections Extra Questions
• Limits And Derivatives Extra Questions
• Permutations And Combinations Extra Questions
• Probability Extra Questions
• Relations And Functions Extra Questions
• Sequences And Series Extra Questions
• Sets Extra Questions
• Straight Lines Extra Questions
• Trigonometric Functions Extra Questions