मराठी

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

प्रश्न

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

बेरीज
Advertisements

उत्तर

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Sets - Exercise 1.3 [पृष्ठ १३]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
पाठ 1 Sets
Exercise 1.3 | Q 9.2 | पृष्ठ १३

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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}


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

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

 


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: 

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

 


For any two sets, prove that: 

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


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


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: 

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


Is it true that for any sets A and \[B, P \left( A \right) \cup P \left( B \right) = P \left( A \cup B \right)\]? Justify your answer.


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


Each set X, contains 5 elements and each set Y, contains 2 elements and \[\cup^{20}_{r = 1} X_r = S = \cup^n_{r = 1} Y_r\] If each element of S belong to exactly 10 of the Xr's and to eactly 4 of Yr's, then find the value of n.


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: 

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


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 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.


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 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 survey of 200 students of a school, it was found that 120 study Mathematics, 90 study Physics and 70 study Chemistry, 40 study Mathematics and Physics, 30 study Physics and Chemistry, 50 study Chemistry and Mathematics and 20 none of these subjects. Find the number of students who study all the three subjects.


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.


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 ______.


Match the following sets for all sets A, B, and C.

Column A Column B
(i) ((A′ ∪ B′) – A)′ (a) A – B
(ii) [B′ ∪ (B′ – A)]′ (b) A
(iii) (A – B) – (B – C) (c) B
(iv) (A – B) ∩ (C – B) (d) (A × B) ∩ (A × C)
(v) A × (B ∩ C) (e) (A × B) ∪ (A × C)
(vi) A × (B ∪ C) (f) (A ∩ C) – B

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×