Question

if A={ x,y,z} then the number of non- empty subsets of A is 1)8. 2) 5 3) 6 4)7 . please tell the answer in step by step .


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Answer 1

$\large\bf\underline {To \: find:-}$

• we need to find number of non - empty sunsets.

$\huge\bf\underline{Solution:-}$

$\bf\underline{\red{Given:-}}$

• A = { x , y ,z}

We know that,

For finding numbers of subsets of set there is a formula :-

$\large \red{ \bf \: subset \: formula: - \: {2}^{n} }$

where ,

• n denots number of elements in a set

In the given set A has 3 elements,

So,

Number of subsets of set A is :-

⇝ 2^n

⇝ 2³

⇝ 2 × 2 × 2

⇝ 8

So, the given set A has 8 Subsets

• A = {x , y ,z}

Subsets of set A are = {x} , {y} , {z} , {xy} , {xz} , {yz} , {x , y, z} , {} .

• {} is a sunset of all sets
• A set is subset of itself.

So,

• Number of non - empty sets is 7

So, Option 4) 7 is correct ✓

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