Question

16. Find the number of subsets of the set F = {a,b,c} and list all the subsets of F.​

Answer 1

1. the subsets of F is A, B, C, AB, BC, CA, null set, ABC so there are 8 subsets of F

Answer 2

$\underline{ \underline{ \bf{ \color{orange}no. \: of \: subsets \: of \: a \: given \: set}}}$

A set containing ' n ' elements have 2ⁿ no. of subsets.

Example :

Let,

A = { x, y, z }

then subsets of A will be

{ } , {x} , {y} , {z} , { x, y} , {y, z} , {x, z} , { x, y, z}

$\underline{ \underline{ \bf{ \color{orange}no. \: of \: proper \: subsets \: of \: a \: set}}}$

A set containing ' n ' elements have 2ⁿ - 1 no. of proper subsets.

( It is because all subsets of any set except the subset itself of that set are proper subset)

Example :

Let,

A = { x, y, z }

then,

proper subsets of A Will be

{ } , {x} , {y} , {z} , { x, y} , { y, z} , { x, z}

$\underline{ \underline{ \bf{ \color{orange}what \: is \: a \: power \: set}}}$

A power set is the set containing all the subsets of a set 'M' including empty set and M itself.

It will be generally denoted as

P(M)

$\underline{ \underline{ \bf{ \color{orange}solution \: to \: question}}}$

Given set

F = { a, b, c}

no. of elemets in F = 3

so,

no. of subsets of F = 2³ = 8

★ Listing all the subsets of F ★

{ } , {a} , {b} , {c} , {a, b} , {b, c} , {c, a} , {a, b, c}