हिंदी

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

Advertisements
Advertisements

प्रश्न

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

रिक्त स्थान भरें
Advertisements

उत्तर

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

Explanation:

Since A – B = A ∩ B'

⇒ A – (A ∩ B) = A ∩ B'

A – B = A ∩ B'

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Sets - Exercise [पृष्ठ १७]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
अध्याय 1 Sets
Exercise | Q 51 | पृष्ठ १७

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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?

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}


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, 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 three sets AB and C, show that \[A \cap B = A \cap C\]


For three sets AB and C, show that \[A \subset B \Rightarrow C - B \subset C - A\] 


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\[A \cap B \cap C = \phi\]


For any two sets A and B, prove that: \[A \cap B = \phi \Rightarrow A \subseteq B'\] 


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: 

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


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:

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


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


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 ∪ D


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


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.


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.


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 ______.


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×