English

Given the sets, A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, the following may be considered as universal set (s) for all the three sets A, B and C? {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Advertisements
Advertisements

Question

Given the sets, A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, the following may be considered as universal set (s) for all the three sets A, B and C?

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Sum
Advertisements

Solution

A ⊂ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

B ⊂ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

C ⊂ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Therefore, the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is the universal set for the sets A, B, and C.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Sets - EXERCISE 1.3 [Page 13]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 1 Sets
EXERCISE 1.3 | Q 8. (iii) | Page 13

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Given the sets, A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, the following may be considered as universal set (s) for all the three sets A, B and C?

{0, 1, 2, 3, 4, 5, 6}


Given the sets, A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, the following may be considered as universal set (s) for all the three sets A, B and C?

Φ


Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, the following may be considered as universal set (s) for all the three sets A, B and C?

{1, 2, 3, 4, 5, 6, 7, 8}


If \[X = \left\{ 8^n - 7n - 1: n \in N \right\} \text{ and } Y = \left\{ 49\left( n - 1 \right): n \in N \right\}\] \[X \subseteq Y .\]


If U = {2, 3, 5, 7, 9} is the universal set and A = {3, 7}, B = {2, 5, 7, 9}, then prove that: 

\[\left( A \cup B \right)' = A' \cap B'\] 


For any two sets A and B, prove that 

 B ⊂ A ∪ B         


For any two sets A and B, prove that A ⊂ B ⇒ A ∩ B = A 


For any two sets A and B, show that the following statements are equivalent:

(i) \[A \subset B\] 

(ii) \[A \subset B\]=ϕ 

(iii) \[A \cup B = B\]

(iv) \[A \cap B = A .\] 


For any two sets, prove that: 

\[A \cup \left( A \cap B \right) = A\] 

 


Find sets A, B and C such that \[A \cap B, A \cap C \text{ and } B \cap C\]are non-empty sets and\[A \cap B \cap C = \phi\]


If A and B are sets, then prove that  \[A - B, A \cap B \text{ and } B - A\] are pair wise disjoint. 


Using properties of sets, show that for any two sets A and B,\[\left( A \cup B \right) \cap \left( A \cap B' \right) = A\] 


For any two sets of A and B, prove that: 

\[B' \subset A' \Rightarrow A \subset B\]


Show that for any sets A and B, A = (A ∩ B) ∪ ( A - B)


Show that for any sets A and B, A ∪ (B – A) = (A ∪ B)


For any two sets A and B, prove that : 

\[A' - B' = B - A\] 


For any two sets A and B, prove the following: 

\[A \cap \left( A' \cup B \right) = A \cap B\] 


For any two sets A and B, prove the following: 

\[A \cap \left( A \cup B \right)' = \phi\] 


Let A and B be two sets such that : \[n \left( A \right) = 20, n \left( A \cup B \right) = 42 \text{ and } n \left( A \cap B \right) = 4\] \[n \left( B - A \right)\]


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


In a survey it was found that 21 persons liked product P1, 26 liked product P2 and 29 liked product P3. If 14 persons liked products P1 and P2; 12 persons liked product P3 and P1 ; 14 persons liked products P2 and P3 and 8 liked all the three products. Find how many liked product P3 only.


Let A and B be two sets in the same universal set. Then,\[A - B =\]


If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

B ∪ C


If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

A ∪ B ∪ C


If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

B ∪ C ∪ D


If X and Y are subsets of the universal set U, then show that Y ⊂ X ∪ Y


If X and Y are subsets of the universal set U, then show that X ∩ Y ⊂ X


If X and Y are subsets of the universal set U, then show that X ⊂ Y ⇒ X ∩ Y = X


If A and B are subsets of the universal set U, then show that A ⊂ A ∪ B


If A and B are subsets of the universal set U, then show that A ⊂ B ⇔ A ∪ B = B


A, B and C are subsets of Universal Set U. If A = {2, 4, 6, 8, 12, 20} B = {3, 6, 9, 12, 15}, C = {5, 10, 15, 20} and U is the set of all whole numbers, draw a Venn diagram showing the relation of U, A, B and C.


Let A, B and C be sets. Then show that A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)


In a town of 10,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B, 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers. Find the number of families which buy newspaper A only.


In a town of 10,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B, 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers. Find the number of families which buy none of A, B and C


Given the sets A = {1, 3, 5}. B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Then the universal set of all the three sets A, B and C can be ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×