Question

If A = {x/x = n2, n = 1,2,3) then find the number of proper subsets of A.​

Answer 1

SOLUTION :

GIVEN

$\sf{}A = \{ \: x : x = {n}^{2} , n =1,2,3 \: \}$

TO DETERMINE

The number of proper subsets of A

CONCEPT TO BE IMPLEMENTED

If a set S contains n elements then the number of proper subsets of S

$\sf{ = {2}^{n} \: - 1 }$

EVALUATION

Here

$\sf{}A = \{ \: x : x = {n}^{2} , n =1,2,3 \: \}$

$\therefore \: \: \sf{}A = \{ \: 1,4,9 \: \}$

So the set A contains 3 elements

$\sf{}n(A )=3$

So the total number of proper subsets of A

$= \sf{} {2}^{3} - 1$

$\sf{} = 8 - 1$

$\sf{} = 7$

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LEARN MORE FROM BRAINLY

If n(A) = 300, n(A∪B) = 500,

n(A∩B) = 50 and n(B′) = 350,

find n(B) and n(U)

https://brainly.in/question/4193770