which one of the following are emply sets? why? a) A{a | a is an natural number smaller than zero} b) B={x | x²=0}
Answers
CONCEPT
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
Empty Set
A set S is said to be Empty set if it contains no elements
EVALUATION
i. A = {a |a is a natural number smaller than zero.}
The set of natural numbers is denoted by N and the set is given by
N = { 1 , 2 , 3 , 4 ,...}
So there is no natural number smaller than zero
So A is an empty set
ii. B = {x | x² = 0}
x² = 0 gives x = 0
B = {x | x² = 0} = { 0 }
So B contains one element
So B is not an empty set
iii. C = { x | 5x – 2 = 0, x ∈ N }
5x – 2 = 0
⇒ x = 2/5
We know that
N = { 1 , 2 , 3 , 4 ,...}
So C is an empty set
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