Question

1. Write in Roster form A = { x: x2 < 30, x EW} Also write number of proper subsets of A.​

Answer 1

SOLUTION

TO DETERMINE

• The Roster form A = { x : x² < 30 , x ∈ W }

• Write number of proper subsets of A.

CONCEPT TO BE IMPLEMENTED

SET :

A set is a well defined collection of distinct objects of our perception or of our thought to be conceived as a whole

Representation of Set

A set can be represented in following ways

(i) Statement form method

(ii) Roster or tabular form method

(iii) Rule or set builder form method

EVALUATION

(i) Here the given set is

A = { x : x² < 30 , x ∈ W }

W is the set of whole numbers

x² < 30

⇒ x = 0 , 1 , 2 , 3 , 4 , 5

Hence the Roster form

A = { x : x² < 30 , x ∈ W }

= { 0 , 1 , 2 , 3 , 4 , 5 }

(ii)

Number of elements in A = 6

So the Number of proper subsets of A

$\sf{ = {2}^{6} - 1 }$

$\sf{ = 64 - 1 }$

$\sf{ = 63}$

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Answer 2

Step-by-step explanation:

Here the given set is

A = { x : x² < 30 , x ∈ W }

W is the set of whole numbers

x² < 30

⇒ x = 0 , 1 , 2 , 3 , 4 , 5

Hence the Roster form

A = { x : x² < 30 , x ∈ W }

= { 0 , 1 , 2 , 3 , 4 , 5 }