Advertisements
Advertisements
प्रश्न
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 chess (Hint: Use Venn diagram)
Advertisements
उत्तर
Let A, B and C represent students play chess, carrom and table tennis.
n(A) = 22, n(B) = 21, n(C) = 15
n(A ∩ C) = 10, n(B ∩ C) = 8, n(A ∩ B ∩ C) = 6
Let “x” represent student play chess and carrom but not table tennis.
Let us represent the data in Venn diagram.
From the Venn diagram we get,
Number of students play atleast one game = 35
12 – x + x + 13 – x + 2 + 6 + 4 + 3 = 35
40 – 35 = x
5 = x
Number of students who play only chess
= 12 – x
= 12 – 5
= 7
APPEARS IN
संबंधित प्रश्न
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)
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(A ∪ D)
State true or false for the following. Correct the wrong statement.
If A = {0}, then n(A) = 0
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 tea
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 class of 50 students, each one come to school by bus or by bicycle or on foot. 25 by bus, 20 by bicycle, 30 on foot and 10 students by all the three. Now how many students come to school exactly by two modes of transport?
If n(A ∪ B ∪ C) = 100, n(A) = 4x, n(B) = 6x, n(C) = 5x, n(A ∩ B) = 20, n(B ∩ C) = 15, n(A ∩ C) = 25 and n(A ∩ B ∩ C) = 10, then the value of x is
For any three sets A, B and C, (A – B) ∩ (B – C) is equal to
The shaded region in the Venn diagram is
What does the "cardinality" of a set represent?
