Advertisements
Advertisements
प्रश्न
What universal set (s) would you propose for the following:
The set of right triangles.
उत्तर १
For the set of right triangles, the universal set can be the set of triangles or the set of polygons.
उत्तर २
Right triangle is a type of triangle. So the set of triangles contain all types of triangles.
∴ U = {x : x is a triangle in a plane)
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}
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}
For any two sets A and B, prove that
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 \[A \subset B \Rightarrow C - B \subset C - A\]
For any two sets, prove that:
\[A \cap \left( A \cup B \right) = A\]
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:
\[B' \subset A' \Rightarrow A \subset B\]
Show that for any sets A and B, A = (A ∩ B) ∪ ( 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:
\[A \cap \left( A \cup B \right)' = \phi\]
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 : \[n \left( A \right) = 20, n \left( A \cup B \right) = 42 \text{ and } n \left( A \cap B \right) = 4\] \[n \left( B - A \right)\]
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 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 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
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 X ⊂ Y ⇒ X ∩ Y = X
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.
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 none of A, B and C
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 ______.
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 |
