MathDB

Find the maximum possible cardinality of S

Source: MTRP 2016 Class 11-Multiple Choice Question: Problem 10 :-

May 31, 2020

Setscardinality

Problem Statement

Let

A=\{1,2,\cdots ,100\}

. Let

S

be a subset of power set of

A

such that any two elements of

S

has nonzero intersection (Note that elements of

S

are actually some subsets of

A

). Then the maximum possible cardinality of

S

is
[*]

2^{99}

[*]

2^{99}+1

[*]

2^{99}+2^{98}

[*] None of these