Home
Class 12
MATHS
Let A(1), A(2),……A(m) be m sets such tha...

Let `A_(1), A_(2),……A_(m)` be m sets such that `O(A_(1))=p, AA i=1,2,….m and B_(1), B_(2)…..B_(n)` be n sets such that `Q(B_(1))=q AA j=1,2,……n`. `"If " underset(i=1)overset(m)UA_(i)=underset(j=1)overset(n)UB_(i)=S` and each of element S belongs to exactly `alpha` number of `A_(i)'s and beta` number of `B_(j)S` then,

A

pm=nq

B

`alphapm=betanq`

C

`betapm=alphanq`

D

`(pm)^(beta)=(nq)^(alpha)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • SETS

    AAKASH INSTITUTE|Exercise SECTION-H(Multiple True-False type Questions)|3 Videos

  • SEQUENCES AND SERIES

    AAKASH INSTITUTE|Exercise Assignment (SECTION - J) Aakash Challengers|12 Videos

  • STATISTICS

    AAKASH INSTITUTE|Exercise Section-C Assertion-Reason|15 Videos

Similar Questions

Explore conceptually related problems

Let A_1 , A_2 , ....., A_m be m sets such that O(A_i) = p for i = 1,2,....,m and B_1 , B_2,....,B_n sets such that O(B_j) = q for j = 1,2,....,n. If uuu_(j=1)^m A_i = uuu_(j=1)^n B_j = S and each element of S belongs to exactly alpha number of A_j's and beta number of B_j's, then

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.

If A_(1),A_(2),..., A_(100) are sets such that n(A_(i))=i+2,A_(1)subA_(2)subA_(3)...subA_(100)and underset(i=3)overset(100)nnA_(i)=A,then n(A)=

Let A_(1),A_(2),A_(3),…, A_(100) be 100 seta and such that n(A_(1))=i+1and A_(1)subA_(2)subA_(3)sub...A_(100),then underset(i=1)overset(100)UAj contains… elements

Suppose A_(1) ,A_(2) ,. . . .,A_(30) are thirty sets each with fvie elements and B_(1),B_(2), .. . .,B_(n) are n sets elements such that bigcup_(i=1)^(30)A_(i)= bigcup _(i=1)^(n)B_(i) and exactly 9 of the B_(j) 's then the value of n , is

Let a_(1),a_(2)…,a_(n) be a non-negative real numbers such that a_(1)+a_(2)+…+a_(n)=m and let S=sum_(iltj) a_(i)a_(j) , then

Knowledge Check

  • Suppose A_(1), A_(2) ,……….. A_(45) sets such that each A_(i) has 6 elements and B_(1), B_(2), ……… B_(n) are n sets each with 3 elements. Let underset(i=1)overset(45)cap A_(i) = underset(j=1)overset(n) cap B_(j) = 5 and each element of S belongs to exactly 10 of the A_(i) 's and exactly 9 of the B_(j) 's. Then n is equal to

    A
    27
    B
    51
    C
    81
    D
    87

  • Suppose A_(1),A_(2) ,………… A_(45) are 45 sets each having 6 elements and B_(1),B_(2) ,............. B_n are n sets each with 3 elements, let underset(i=1)overset(45)cup A_(i) = underset(j=1)overset(n)cup B_(j) = S and each element of S belongs to exactly 10 of the A_(i)'s and exactly 9 of the B_(j)s . Then n is equal to

    A
    27
    B
    51
    C
    81
    D
    87

  • Suppose A_(1),A_(2),…,A_(30) are thirty sets each having 5 elements and B_(1),B_(2),…,B_(n) are n sets each with 3 elements, let underset("i = 1")(uu)A_(i)=underset("j = 1")(uu)B_(j)=S and each elements of S belongs to exactly 10 of the A_(i)'s and exactly 9 of the B_(j)'s . Then n is equal to

    A
    15
    B
    3
    C
    45
    D
    None of these