THE TOTAL NO OF SUBSETS OF A FINITE SET CONTAINING n ELEMENTS IS 2n How Plz - Maths - Sets

Question

THE TOTAL NO OF SUBSETS OF A FINITE SET CONTAINING n
ELEMENTS IS 2 n How ?
Plz proove it
ANURAG

Shridhar Kaushik · Accepted Answer

Let A be a finite set containing n elements

Let 0 ≤ r ≤ n

Consider those subsets of A that have r elements each.

We know that the number of ways in which r elements can be chosen out of n elements is ${}^{n}{C_{r}}$ [You will study this concept in chapter combination]

∴ Number of subsets of A having r elements each is ${}^{n}{C_{r}}$

Hence, total number of subsets of A

$= {}^{n}{C_{0}} + {}^{n}{C_{1}} + {}^{n}{C_{2}} + ... + {}^{n}{C_{n}} = (1 + 1)^{n} [Using Binomial Theorem] = 2^{n}$

1

THE TOTAL NO. OF SUBSETS OF A FINITE SET CONTAINING n ELEMENTS IS 2 n . How ? Plz. proove it. ANURAG.

THE TOTAL NO. OF SUBSETS OF A FINITE SET CONTAINING n ELEMENTS IS 2 ⁿ. How ?

Plz. proove it.

ANURAG.