Question

If n( A×B ) =24 , n[p (B) ] =64, then n(A) is :
a) 2
b ) 3
c) 6
d) 4
CORRECT answer only​

Answer 1

Answer:

d) 4

Step-by-step explanation:

n[p(B)] = 2^x

64 = 2^x , where x=6 ( as 2^6 = 64 )

therefore, n(B) = 6

n( A × B ) = n (A) × n (B)

24 = n (A) × 6

therefore, n (A) = 4.

Answer 2

The value of n(A) = 4

Given :

n(A × B) = 24 , n[P(B)] = 64

To find :

The value of n(A) is

a) 2

b ) 3

c) 6

d) 4

Solution :

Step 1 of 3 :

Calculate number of elements in B

The collection of all subsets of a non empty set B is a set of sets. This set is called the power set B and is denoted by P(B)

Let the number of elements in the set B = n

Then the number of elements in power set of B = n[P(B)] = 2ⁿ

By the given condition

$\displaystyle \sf{ {2}^{n} = 64 }$

$\displaystyle \sf{ \implies {2}^{n} = {2}^{6} }$

$\displaystyle \sf{ \implies n = 6}$

∴ Number of elements in the set B = 6

Step 2 of 3 :

Calculate number of elements in A

Here it is given that ,

n(A × B) = 24

⇒ n(A) × n(B) = 24

⇒ n(A) × 6 = 24

⇒ n(A) = 24/6

⇒ n(A) = 4

∴ Number of elements in A = n(A) = 4

Step 3 of 3 :

Choose the correct option

Checking for option (a)

Since number of elements in A = n(A) = 4

So option (a) is not correct

Checking for option (b)

Since number of elements in A = n(A) = 4

So option (b) is not correct

Checking for option (c)

Since number of elements in A = n(A) = 4

So option (c) is not correct

Checking for option (d)

Since number of elements in A = n(A) = 4

So option (d) is correct

Final answer : Hence the correct option is d) 4

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