हिंदी

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} - 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?

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

योग
Advertisements

उत्तर

It can be seen that A ⊂ {0, 1, 2, 3, 4, 5, 6}

B ⊂ {0, 1, 2, 3, 4, 5, 6}

However, C ⊄ {0, 1, 2, 3, 4, 5, 6}

Therefore, the set {0, 1, 2, 3, 4, 5, 6} cannot be the universal set for the sets A, B, and C.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Sets - Exercise 1.3 [पृष्ठ १३]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
अध्याय 1 Sets
Exercise 1.3 | Q 9.1 | पृष्ठ १३

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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

The set of right 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?

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?

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


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 

A ∩ ⊂ A             


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


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


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 = (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: 

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


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


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


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

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


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


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


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.


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 ______.


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 ______.


For all sets A and B, A – (A ∩ B) is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×