English

If a and B Are Two Set Such that a ⊂ B Then Find: a ∩ B - Mathematics

Advertisements
Advertisements

Question

If A and B are two set such that \[A \subset B\]then find: 

\[A \cap B\]

 

Solution

From the Venn diagrams given below, we can clearly say that if A and B are two sets such that \[A \subset B\] then 

Form the given Venn diagram, we can see that \[A \cap B\]= A

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Sets - Exercise 1.05 [Page 21]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 1 Sets
Exercise 1.05 | Q 1.1 | Page 21

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

If A and B are two sets such that \[A \subset B\] then find: 

\[A \cup B\]


If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14}, find: 

\[A \cup C\]


If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14}, find:

\[B \cup C \cup D\]

 


Let \[A = \left\{ x: x \in N \right\}, B = \left\{ x: x - 2n, n \in N \right\}, C = \left\{ x: x = 2n - 1, n \in N \right\}\] and D = {x : x is a prime natural number}. Find: \[A \cap C\] 

 


Let \[A = \left\{ x: x \in N \right\}, B = \left\{ x: x - 2n, n \in N \right\}, C = \left\{ x: x = 2n - 1, n \in N \right\}\] and D = {x : x is a prime natural number}. Find: \[B \cap D\]


Let \[A = \left\{ x: x \in N \right\}, B = \left\{ x: x - 2n, n \in N \right\}, C = \left\{ x: x = 2n - 1, n \in N \right\}\] and D = {x : x is a prime natural number}. Find: \[C \cap D\]


Let A = {3, 6, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16} and D = {5, 10, 15, 20}. Find: \[A - D\] 


Represent the union of two sets by Venn diagram for the following.

A = {3, 4, 5, 7}  B = {1, 4, 8}


Represent the union of two sets by Venn diagram for the following.

P = {a, b, c, e, f} Q = {l, m, n, e, b}


Represent the union of two sets by Venn diagram for the following.

X = {x | x is a prime number between 80 and 100}

Y = {y | y is an odd number between 90 and 100}


Express the truth of each of the following statements using Venn diagrams: 

(a) No circles are polygons

(b) Some quadratic equations have equal roots 


Express the truth of the following statements with the help of Venn diagram:
(a) No circles are polygon
(b) If a quadrilateral is rhombus , then it is a parallelogram .


Express the truth of each of the following statements by Venn diagram :
(a) Some hardworking students are obedient.
(b) No circles are polygons.
(c) All teachers are scholars and scholars are teachers.


From the given diagram find : 
A' ∩ B


From the given diagram find : 
A - B


From the given diagram find : 
B - A


From the given diagram, find: 
(i) A’ 
(ii) B’ 
(iii) A' ∪ B' 
(iv) (A ∩ B)'

Is A' ∪ B' = (A ∩ B)' ?

Also, verify if A' ∪ B' = (A ∩ B)'.


Use the given diagram to find:

(i) A ∪ (B ∩ C)

(ii) B - (A - C)

(iii) A - B

(iv) A ∩ B'

Is A ∩ B' = A - B?


Use the given Venn-diagram to find :
A


Use the given Venn-diagram to find :
B'


Use the given Venn-diagram to find :
A ∩ B


Use the given Venn-diagram to find :
A ∪ B


Two sets A and B are such that A ∩ B = Φ. Draw a venn-diagram to show the relationship between A and B. Shade the region representing :
B ∩ A'


State the sets representing by the shaded portion of following venn-diagram :


In the given diagram, shade the region which represents the set given underneath the diagrams: (P ∩ Q)'


Using the given diagram, express the following sets in the terms of A and B. {a, d, c, f, g, h}


Using the given diagram, express the following sets in the terms of A and B. {g, h}


Represent the truth of the following statement by the Venn diagram.

No circles are polygons.


Draw a Venn diagram for the truth of the following statement.

Some share brokers are chartered accountants.


Represent the following statement by the Venn diagram.

No circle is rectangle.


Draw the Venn diagrams to illustrate the following relationship among sets E, M and U, where E is the set of students studying English in a school, M is the set of students studying Mathematics in the same school, U is the set of all students in that school.

Some of the students study Mathematics but do not study English, some study English but do not study Mathematics, and some study both.


Draw Venn diagram for the following:

No policeman is thief


Take the set of natural numbers from 1 to 20 as universal set and show set X using Venn diagram.

X = {x | x ∈ N, and 7 < x < 15}


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×