Question

find all the subset of each of the following sets number one is done for you.
1. A={m,n,p}. ( m),(n),(p),(m,n),. (m,p),(n,p),(m,n,p).

2. B=(x,y)

3. C=(1,2,8)

4. D=(a,b,c,d)

5. E=(a)



hope someone will answer

Answer 1

Answer:

2. { φ, {x},{y},{x,y} }

3. { φ, {1},{2},{3},{1,2},{2,3},{3,1},{1,2,3} }

4. {φ, {a},{b},{c},{d},{a,b},{b,c},{c,d},{b,d},{a,c},{a,d},{a,b,c},{b,c,d}, {a,b,d},{a,c,d},{a,b,c,d} }

5. {φ,{a} }

Answer 2

Subsets are:

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

{} , {1} , {2} , { 8} , { 1 , 2} , {1  , 8} , {2 , 8} , {1 , 2, 8 }

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

{} , {a}

Given:

• Set A = {m , n , p}
• Subsets {} , {m} , {n} , (m , n} , ( m,p} , {n , p} , {m , n , p}

To Find:

• Subsets of Each of the following set
• B = { x , y}
• C = { 1 , 2 , 8}
• D = { a , b , c , d}
• E = { a}

Solution

• Number of subsets of a set with n elements is 2ⁿ

Step 1:

B = { x , y}

n(B) = 2

Number of subsets = 2² = 4

Subsets = {} , {x} , {y} , { x , y}

{} represent null/empty set , this can be represented as ∅ also

Step 3:

C = { 1 , 2 , 8}

n(C) = 3

Number of subsets = 2³ = 8

Subsets = {} , {1} , {2} , { 8} , { 1 , 2} , {1  , 8} , {2 , 8} , {1 , 2, 8 }

Step 3:

D= { a, b, c, d}

n(D) = 24

Number of subsets = 2⁴ = 16

Subsets = {} , {a} , {b} , {c} , {d} , { a , b} , {a , c} , {a , d} ,{b , c} , {b , d} , { c , d} ,{a, b , c} , { a, b , d} , {a , c , d} , { b, c , d} , { a, b , c , d }

Step 4:

E = { a}

n(E) = 1

Number of subsets = 2¹= 2

Subsets = {} , {a}

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