Question

let A and B br two set containing 4 element and 2 element respectively . then the number of subset of sets A*B each having atleast three element is ?​

Answer 1

To find :

• we need to find the number of subsets in A × B

Solution :

• n(A) = 4
• n(B) = 2

We know that,

✫ n(A × B) = n(A) × n(B)

➔ n(A × B) = 4 × 2

➔ n(A × B) = 8

As We know that

Number of Subsets = 2^n

where n shows number of elements .

Finding number of subsets in A × B

➔ n(A × B) = 8

So,

• A × B has 8 elements

Number of subsets in A × B :-

• n = 8

= 2⁸

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 16 × 16

= 256

Hence,

• A × B has 256 subsets.

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Answer 2

$\bf{\underline{Question:-}}$

let A and B br two set containing 4 element and 2 element respectively . then the number of subset of sets A*B each having atleast three element is ?

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

Given,

• n(A) = 4
• n(B) = 2

then the number of subset of sets A*B each having atleast three element is.

$\sf → 2^8 - ^8C_0 - ^8 C_2$

$\sf → 256 - 1 - 8 - 28$

$\bf → 219$

$\bf{\underline{Hence:-}}$

• A × B has 219 subsets.