Advertisements
Advertisements
Question
In a party of 45 people, each one likes tea or coffee or both. 35 people like tea and 20 people like coffee. Find the number of people who do not like coffee
Solution
Let ’T’ be the set of people like Tea
Let ‘C’ be the set of people like Coffee
n(T ∩ C) = 45, n(T) = 35 and n(C) = 20
Let X be the number of people like both Tea and Coffee.
By using the Venn-diagram
From the Venn-diagram we get.
35 – x + x + 20 – x = 45
55 – x = 45
55 – 45 = x
10 = x
People do not like coffee
= 35 – x
= 35 – 10
= 25
APPEARS IN
RELATED QUESTIONS
State, whether the pair of sets, given below, are equal sets or equivalent sets:
{2, 4, 6, 8, 10} and {a, b, d, e, m}
Write the cardinal number of the following set:
A = {0, 1, 2, 4}
Given:
A = {Natural numbers less than 10}
B = {Letters of the word ‘PUPPET’}
C = {Squares of first four whole numbers}
D = {Odd numbers divisible by 2}.
Find: n(D)
Given:
A = {Natural numbers less than 10}
B = {Letters of the word ‘PUPPET’}
C = {Squares of first four whole numbers}
D = {Odd numbers divisible by 2}.
Find: n(B ∪ D)
State true or false for the following. Correct the wrong statement.
If A = {0}, then n(A) = 0
If n(A) = 25, n(B) = 40, n(A ∪ B) = 50 and n(B’) = 25, find n(A ∩ B) and n(U).
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 an examination 50% of the students passed in Mathematics and 70% of students passed in Science while 10% students failed in both subjects. 300 students passed in both the subjects. Find the total number of students who appeared in the examination, if they took examination in only two subjects
In the adjacent diagram, if n(U) = 125, y is two times of x and z is 10 more than x, then find the value of x, y and z
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)
