Advertisements
Advertisements
प्रश्न
For all sets A and B, A – (A ∩ B) is equal to ______.
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'
APPEARS IN
संबंधित प्रश्न
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}
If U = {2, 3, 5, 7, 9} is the universal set and A = {3, 7}, B = {2, 5, 7, 9}, then prove that:
\[\left( A \cup B \right)' = A' \cap B'\]
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 three sets A, B and C, show that \[A \cap B = A \cap C\]
For three sets A, B and C, show that \[A \subset B \Rightarrow C - B \subset C - A\]
For any two sets, prove that:
\[A \cup \left( A \cap B \right) = A\]
Find sets A, B and C such that \[A \cap B, A \cap C \text{ and } B \cap C\]are non-empty sets and\[A \cap B \cap C = \phi\]
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,\[\left( A \cup B \right) \cap \left( A \cap B' \right) = A\]
Show that for any sets A and B, A = (A ∩ B) ∪ ( 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 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 : \[n \left( A \right) = 20, n \left( A \cup B \right) = 42 \text{ and } n \left( A \cap B \right) = 4\] \[n \left( B - A \right)\]
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 group of 950 persons, 750 can speak Hindi and 460 can speak English. Find:
how many can speak English 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 A, B 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 \[n \left( A' \cap B' \right) =\]
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 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 ⊂ B ⇔ A ∪ B = B
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.
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 ______.
