Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Total number of families = 10000
⇒ n(U) = 10000
Number of families who buy newspaper A = 40%
⇒ n(A) = 40%
Number of families who buy newspaper B = 20%
⇒ n(B) = 20%
Number of families who buy newspaper C = 10%
⇒ n(C) = 10%
Number of families who buy newspapers A and B = 5%
⇒ n(A ∩ B) = 5%
Number of families who buy newspapers B and C = 3%
⇒ n(B ∩ C) = 3%
Number of families who buy newspapers A and C = 4%
⇒ n(A ∩ C) = 4%
Number of families who buy all the three newspapers = 2%
⇒ n(A ∩ B ∩ C) = 2%
Number of families who buy newspaper A only
= n(A) – n(A ∩ B) – n(A ∩ C) + n(A ∩ B ∩ C)
= `40/100 - 5/100 - 4/100 + 2/100`
= `33/100`
= `10000 xx 33/100`
= 3300 families
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, 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 \[X = \left\{ 8^n - 7n - 1: n \in N \right\} \text{ and } Y = \left\{ 49\left( n - 1 \right): n \in N \right\}\] \[X \subseteq Y .\]
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
A ∩ B ⊂ A
For any two sets A and B, prove that A ⊂ B ⇒ A ∩ B = A
For any two sets, prove that:
\[A \cup \left( A \cap B \right) = A\]
For any two sets, prove that:
\[A \cap \left( A \cup B \right) = A\]
If A and B are sets, then prove that \[A - B, A \cap B \text{ and } B - A\] are pair wise disjoint.
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:
\[A \cap \left( A' \cup B \right) = A \cap B\]
For any two sets A and B, prove the following:
\[A - \left( A - B \right) = A \cap B\]
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 : \[n \left( A \right) = 20, n \left( A \cup B \right) = 42 \text{ and } n \left( A \cap B \right) = 4\] \[n \left( B - A \right)\]
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 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 ∪ D
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 ∪ D
If X and Y are subsets of the universal set U, then show that X ∩ Y ⊂ X
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
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
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 ______.
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 |
