Suppose `A_1,A_2….. A_(30)` are thirty sets each having 5 elements and `B_1B_2…..B_n` are n sets each having 3 elements ,Let `overset(30)underset(i=1)bigcupA_1=overset(n)underset(j=1)bigcupB_j=s` and each element of S belongs to exactly 10 of the `A_1` and exactly 9 of the value of n.
Text Solution
Verified by Experts
If elements are not repeated , then number of elements in `A_1 cup A_2 cup A_3 ……cup A_30 xx5 =150 .` but each elements of S is used 10 times in `A_i` s so `s=(30xx5)/(10)` If elements in `B_1 cup B_2 cup B_3 ….cup B_n` is 3n But each elements of S is repeated 9 time in `B_j` s so `S=(3n)/(9) rArr 15 = (3n)/(9)` `therefore n=45`
Topper's Solved these Questions
SET THEORY AND REAL NUMBER SYSTEM
CENGAGE|Exercise Exercise 1.1|12 Videos
SET THEORY AND REAL NUMBER SYSTEM
CENGAGE|Exercise Exercise 1.2|8 Videos
SEQUENCE AND SERIES
CENGAGE|Exercise Question Bank|1 Videos
SETS AND RELATIONS
CENGAGE|Exercise Question Bank|3 Videos
Similar Questions
Explore conceptually related problems
Prove that underset(rles)(underset(r=0)overset(s)(sum)underset(s=1)overset(n)(sum))""^(n)C_(s) ""^(s)C_(r)=3^(n)-1 .
Let A and B be two sets having m and n elements respectively . Then total number of functions from A to B is
Find the number of all three elements subsets of the set {a_1, a_2, a_3, a_n} which contain a_3dot
The value of Sigma_(i=1)^(n) Sigma_(j=1)^(i) underset(k=1)overset(j) =220, then the value of n equals
A_1,A_2,..., A_n are the vertices of a regular plane polygon with n sides and O as its centre. Show that sum_(i=1)^n vec (OA)_i xx vec(OA)_(i+1)=(1-n)(vec (OA)_2 xx vec(OA)_1)
Let A_1,A_2,....A_n be the vertices of an n-sided regular polygon such that , 1/(A_1A_2)=1/(A_1A_3)+1/(A_1A_4) . Find the value of n.
Let {a_n}(ngeq1) be a sequence such that a_1=1,a n d3a_(n+1)-3a_n=1 for all ngeq1. Then find the value of a_(2002.)
If a_(n+1)=1/(1-a_n) for n>=1 and a_3=a_1 . then find the value of (a_2001)^2001 .
CENGAGE-SET THEORY AND REAL NUMBER SYSTEM -Archieves
