Question

10. Let A = Square, rectangle, triangle } Find the following
(i) n (A) () n p (A)] (iii) Number of proper subsets of A​

Answer 1

Answer:

1) 3

3) 8

Step-by-step explanation:

number of subsets=2^n

Answer 2

Step-by-step explanation:

Given:-

A = {Square, rectangle, triangle }

To find:-

Find the following:

(i) n (A)

(ii) n [p (A)]

(iii) Number of proper subsets of A

Solution:-

Given set : A = { Square, rectangle, triangle }

Number of elements in the set A = 3

n(A) = 3

We know that

If the number of elements of a set n then the number of subsets = 2^n

n(A) = 3 then Number of subsets are 2^3 = 8

n[p(A)] = 8

We know that

If a set contains n elements, then the number of subsets of this set is equal to 2^n - 1 .

n(A) = 3 then Number of proper subsets of A

=> 2^3 -1

=> 8-1

=> 7

number of proper subsets = 7

Answer:-

I) Number of elements in A = n(A)=3

ii) Number of subsets to A = n[p(A)] = 8

iii) Number of proper subsets to A = 7

Used formulae:-

• The number of elements in a set A is called The Cardinal number of A and it is denoted by n(A).

• If the number of elements in the set is n then the number of all subsets = 2^n

• If the number of elements in the set is n then the number of all proper subsets = 2^n -1