Advertisements
Advertisements
प्रश्न
A survey shows that 76% of the Indians like oranges, whereas 62% like bananas. What percentage of the Indians like both oranges and bananas?
Advertisements
उत्तर
Let A & B denote the sets of the Indians who like oranges & bananas, respectively.
\[\text{ Given }: \]
\[n\left( A \right) = 76 % \]
\[n\left( B \right) = 62 % \]
\[n\left( A \cup B \right) = 100 % \]
\[n\left( A \cap B \right) = ?\]
\[ \text{ We know }: \]
\[n\left( A \cup B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cap B \right)\]
\[ \Rightarrow 100 = 76 + 62 - n\left( A \cap B \right)\]
\[ \Rightarrow n\left( A \cap B \right) = 38\]
\[\text{ Therefore, 38 % of the Indians like both oranges & bananas } .\]
APPEARS IN
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?
{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
If \[X = \left\{ 8^n - 7n - 1: n \in N \right\} \text{ and } Y = \left\{ 49\left( n - 1 \right): n \in N \right\}\] \[X \subseteq Y .\]
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, prove that
A ∩ B ⊂ A
For any two sets A and B, prove that A ⊂ B ⇒ A ∩ 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:
\[A \cap \left( A \cup B \right) = A\]
For any two sets of A and B, prove that:
\[A' \cup B = U \Rightarrow A \subset B\]
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:
\[A \cap \left( A \cup B \right)' = \phi\]
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 A and B be two sets in the same universal set. Then,\[A - B =\]
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 ∪ 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
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 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 ______.
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 ______.
