English

If a and B Are Two Sets Such that a ⊂ B Then Find: a ∪ B - Mathematics

Advertisements
Advertisements

Question

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

\[A \cup B\]

Advertisements

Solution

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

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

 

 

 

 

 

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 1.2 | Page 21

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Draw appropriate Venn diagram for the following:

(A ∪ B)'


Draw appropriate Venn diagram for the following:

A' ∩ B'


Draw appropriate Venn diagram for the following:

A' ∪ B'


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

\[A \cap B\]

 


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:  

\[B \cup C\]


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: 

\[A \cup B \cup C\]

 


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: 

\[A \cup B \cup D\]


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: \[A \cap D\]

 


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: \[B \cap C\]


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: \[A - C\] 


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: \[A - D\] 


U = {1, 2, 3, 7, 8, 9, 10, 11, 12}
P = {1, 3, 7, 10} then
  1. show the sets U, P and P' by the Venn diagram.
  2. Verify (P')' = P

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

A = {3, 4, 5, 7}  B = {1, 4, 8}


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 .


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 :
B'


Draw a Venn-diagram to show the relationship between two overlapping sets A and B. Now shade the region representing :
A ∩ B


Draw a Venn-diagram to show the relationship between two sets A and B; such that A ⊆ B, Now shade the region representing :
B' ∩ A


Draw a Venn-diagram to show the relationship between two sets A and B; such that A ⊆ B, Now shade the region representing :
(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 :
(A ∪ B)'


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


From the given diagram, find :
(i) (A ∪ B) - C

(ii) B - (A ∩ C)

(iii) (B ∩ C) ∪ A

Verify :
A - (B ∩ C) = (A - B) ∪ (A - C) 


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



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


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

No circles are polygons.


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

All teachers are scholars and scholars are teachers.


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

Some persons are not politician.


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

No child is an adult.


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.

All the students who study Mathematics study English, but some students who study English do not study Mathematics.


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.

Not all students study Mathematics, but every students studying English studies Mathematics.


Let U be the set of all boys and girls in a school, G be the set of all girls in the school, B be the set of all boys in the school, and S be the set of all students in the school who take swimming. Some, but not all, students in the school take swimming. Draw a Venn diagram showing one of the possible interrelationship among sets U, G, B and S.


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×