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? Φ - Mathematics

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?

Φ

Sum

Solution

A ⊄ Φ, B ⊄ Φ, C ⊄ Φ

Φ is a set that contains no elements. So, it is not a universal set for 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 9.2 | Page 13

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

What universal set (s) would you propose for the following:

The set of right triangles.


What universal set (s) would you propose for the following:

The set of isosceles triangles.


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}


For any two sets A and B, prove that 

 B ⊂ A ∪ B         


For any two sets A and B, prove that 

A ∩ ⊂ A             


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


For any two sets, prove that: 

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

 


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: 

\[A' \cup B = U \Rightarrow A \subset B\] 


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)


For any two sets A and B, prove that : 

\[A' - B' = B - A\] 


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

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


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

\[A - B = A \Delta\left( A \cap B \right)\]


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


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


A survey shows that 76% of the Indians like oranges, whereas 62% like bananas. What percentage of the Indians like both oranges and bananas? 


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 U be the universal set containing 700 elements. If AB are sub-sets of U such that \[n \left( A \right) = 200, n \left( B \right) = 300 \text{ and } \left( A \cap B \right) = 100\].Then \[n \left( A' \cap B' \right) =\] 


Let A and B be two sets that \[n \left( A \right) = 16, n \left( B \right) = 14, n \left( A \cup B \right) = 25\] Then, \[n \left( A \cap B \right)\] 


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

A ∪ B ∪ D


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


If A and B are subsets of the universal set U, then show that A ⊂ A ∪ 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 none of A, B and C


The set (A ∩ B′)′ ∪ (B ∩ C) is equal to ______.


If A = {1, 3, 5, 7, 9, 11, 13, 15, 17} B = {2, 4, ..., 18} and N the set of natural numbers is the universal set, then A′ ∪ (A ∪ B) ∩ B′) is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×