Advertisements
Advertisements
प्रश्न
Verify n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C) for the following sets
A = {a, c, e, f, h}, B = {c, d, e, f} and C = {a, b, c, f}
Advertisements
उत्तर
A ∩ B = {a, c, e, f, h} ∩ {c, d, e, f}
= {c, e, f}
B ∩ C = {c, d, e, f} ∩ {a, b, c, f}
= {c, f}
A ∩ C = {a, c, e, f, h} ∩ {a, b, c, f}
= {c, f}
(A ∩ B ∩ C) = {a, c, e, f, h} ∩ {c, d, e, f} ∩ {a, b, c, f}
= {c, f}
(A ∪ B ∪ C) = {a, c, e, f, h} ∪ {c, d, e, f} ∪ {a, b, c, f}
= {a, b, c, d, e, f, h}
n(A ∩ B) = 3, n(B ∩ C) = 2, n(A ∩ C) = 3, n(A ∩ B ∩ C) = 2
n(A ∪ B ∪ C) = 7 ...(1)
n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C)
= 5 + 4 + 4 – 3 – 2 – 3 + 2
= 15 – 8
= 7 ...(2)
From (1) and (2) we get
n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C)
APPEARS IN
संबंधित प्रश्न
State, whether the pair of sets, given below, are equal sets or equivalent sets:
{7, 7, 2, 1,2} and {1, 2, 7}
Write the cardinal number of the following set:
C = { }
Write the cardinal number of the following set:
D= {3, 2, 2, 1, 3, 1, 2}
Write the cardinal number of the following set:
E = {16, 17, 18 19}
State true or false for the following. Correct the wrong statement.
If A = {0}, then n(A) = 0
State true or false for the following. Correct the wrong statement.
n(Φ) = 1
Verify n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C) for the following sets
A = {1, 3, 5}, B = {2, 3, 5, 6}, C = {1, 5, 6, 7}
In a colony, 275 families buy Tamil newspaper, 150 families buy English newspaper, 45 families buy Hindi newspaper, 125 families buy Tamil and English newspaper, 17 families buy English and Hindi newspapers, 5 families buy Tamil and Hindi newspaper and 3 families buy all the three newspaper. If each family buy atleast one of these newspaper then find Number of families buy only one newspaper
Each student in a class of 35 plays atleast one game among chess, carrom and table tennis. 22 play chess, 21 play carrom, 15 play table tennis, 10 play chess and table tennis, 8 play carrom and table tennis and 6 play all the three games. Find the number of students who play only carrom (Hint: Use Venn diagram)
In a city, 40% people like only one fruit, 35% people like only two fruits, 20% people like all the three fruits. How many percentage of people do not like any one of the above three fruits?
