Question

List all the subsets of the following sets c={x,y,z}

Answer 1

All  subsets of the set c={x,y,z}​  are { } , {x } , { y} , { z} ,  {x , y} , { x , z} , { y, z} ,  {x , y , z}  

Given:

Set c = { x , y , z}

To Find:

All the subsets

Solution:

Any set with n elements has 2ⁿ subsets

Subsets consist of 0 to n elements

Number of subsets with x elements are ⁿCₓ  ( 0 ≤ x ≤ n)

Step 1:

Check number of elements in the given set c = { x , y , z }

n = 3

Hence Number of subsets = 2³ = 8

Subsets will consist of 0 to 3 elements

Step 2:

List Subsets with 0 elements     ³C₀ = 1

= { }

= $\phi$

Also Called null set

Step 2:

List  Subsets with 1 element      ³C₁ = 3

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

Step 3:

List  Subsets with 2 element      ³C₂ = 3

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

Step 4:

List  Subsets with 3 element      ³C₃ = 1

= {x , y , z}  

Step 5:

Combine all the Subsets  

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

All  subsets of the set c={x,y,z}​  are { } , {x } , { y} , { z} ,  {x , y} , { x , z} , { y, z} ,  {x , y , z}  

Answer 2

Answer:

All subsets of the set c={x,y,z} are { } , {x } , { y} , { z} , {x , y} , { x , z} , { y, z} , {x , y , z}

Step-by-step explanation:

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