Question

Solve the question in detail.

Answer 1

Answer:

32

Step-by-step explanation:

Given set A = { 1 , 2 , 3 , 4 , 5 }

➯ total number of element in A = 5

➯ n(A) = 5

● we know that numbe of element in

the power set of A = 2ⁿ ( where n is

number of element in A)

➯ so , that —

• number of element in power set = 2⁵

• number of element in power set = 32

⍟⍟⍟ Hence, option (2) is correct. ⍟⍟⍟

Answer 2

Let us say Set A = { a, b, c }

Number of elements: 3

Therefore, the subsets of the set are:

{ } which is the null or the empty set

{ a }

{ b }

{ c }

{ a, b }

{ b, c }

{ c, d }

{ a, b, c }

The power set P(A) = { { } , { a }, { b }, { c }, { a, b }, { b, c }, { c, d }, { a, b, c } }

Now, the Power Set should have 2^3 = 8 elements.

(1 2 3 4 5)

Number of elements: 5

Therefore, the subsets of the set are:

{ } which is the null or the empty set

(1)

(2)

(3)

(4)

(5)

(1 2)

(2 3)

(3 4)

(4 5)

(1 2 3)

(2 3 4)

(3 4 5)

(1 2 3 4)

(2 3 4 5)

(1 2 3 4 5)

(1 3)

(1 4)

(1 5)

(2 4)

(2 5)

(3 5)

(1 3 4 5)

(1 2 4 5)

(1 2 3 5)

(2 4 5)

(1 4 5)

(1 3 4)

(1 2 4)

(1 2 5)

(1 3 5)

(2 3 5)

The power set P(A) =( ) (1) (2) (3) (4) (5) (1 2) (2 3)(3 4) (4 5) (1 2 3) (2 3 4) (3 4 5) (1 2 3 4) (2 3 4 5) (1 2 3 4 5) (1 3) (1 4) (1 5) (2 4) (2 5) (3 5) (1 3 4 5) (1 2 4 5) (1 2 3 5) (2 4 5) (1 4 5) (1 3 4) (1 2 4) (1 2 5) (1 3 5) (2 3 5)

Now, the Power Set should have 2^n

where n is equal to no.of elements in matrix.

the Power Set shouldyou represented should also have 2^n elements = 2^5=32 elements.

Hope it helps you.