Advertisements
Advertisements
प्रश्न
If U = {2, 3, 5, 7, 9} is the universal set and A = {3, 7}, B = {2, 5, 7, 9}, then prove that:
\[\left( A \cap B \right)' = A'B' .\]
Advertisements
उत्तर
Given:
U = {2, 3, 5, 7, 9}
A = {3, 7}
B = {2, 5, 7, 9}
To prove :
\[\left( A \cap B \right)' = A' \cup B'\]
Proof :
LHS:
\[(A \cap B) = {7}\]
\[(A \cap B)' = {2, 3, 5, 9}\]
RHS:
\[A' = {2, 5, 9}\]
\[B' = {3}\]
\[A' \cup B' = {2, 3, 5, 9}\]
LHS = RHS
∴ \[\left( A \cap B \right)' = A' \cup B'\]
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.
If U = {2, 3, 5, 7, 9} is the universal set and A = {3, 7}, B = {2, 5, 7, 9}, then prove that:
\[\left( A \cup B \right)' = A' \cap B'\]
For any two sets A and B, prove that A ⊂ B ⇒ A ∩ B = A
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 A, B and C, show that \[A \cap B = A \cap C\]
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 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: \[A \cap B = \phi \Rightarrow A \subseteq B'\]
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)
For any two sets A and B, prove the following:
\[A \cap \left( A' \cup B \right) = A \cap B\]
Let A and B be two sets such that : \[n \left( A \right) = 20, n \left( A \cup B \right) = 42 \text{ and } n \left( A \cap B \right) = 4\] \[n \left( B - A \right)\]
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 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
B ∪ C
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 ⊂ A ∪ B
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)
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 ______.
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 |
