Question

Let A = {1, 2 }, B = {3, 4} . Find n(P(A X B))

Answer 1

Answer:

n(A×B) =4

your answer is this

Answer 2

Step-by-step explanation:

Given :-

A = {1, 2 },

B = {3, 4}

To find :-

Find n(P(A X B)) ?

Solution :-

Given sets are :

A = {1, 2 }

B = {3, 4}

A X B = { 1, 2 } X { 3, 4 }

=> A X B = { (1,3),(1,4),(2,3),(2,4) }

Number of elements in A X B = 4

n (A X B ) = 4

We know that

The number of subsets of a set of 'n' elements is 2^n

We have, n = 4

So, The number of subsets of A X B = 2^4

=> 2×2×2×2

=> 16

We know that

The number of sub sets of a set A =n( P(A))

The number of subsets of the set A X B

= n(P(A X B)) = 16

Answer:-

The value of n(P(A X B)) for the given problem is 16

Used formulae:-

Let A and B are two non empty sets,

• The set containing order pairs such that first element belongs to A and second element belongs to B is called the Cartesian product of the sets A and B.
• A X B = {(a,b)/ a€ A , b € B}
• € = belongs to
• The number of elements in a set A is called the Cardinal number of A and it is denoted by n(A).
• If n(A) = m and n(B) = n then n(A×B) = mn
• The number of subsets of a set of 'n' elements is 2^n
• The set of all subsets is called the Power set.
• The Power set of the set A is P(A) .