Which of the following would be an empty set? a. The set of odd numbers that are divisible by 2 b. The set of prime numbers that are odd numbers c. The set of even numbers that are prime numbers d. The set of multiplies of 3 that are prime numbers
Answers
Answer:
The correct answer which is an empty set is the option (A) A set of odd numbers which are divisible by 2.
SOLUTION
TO CHOOSE THE CORRECT OPTION
Which of the following would be an empty set
a. The set of odd numbers that are divisible by 2
b. The set of prime numbers that are odd numbers
c. The set of even numbers that are prime numbers
d. The set of multiplies of 3 that are prime numbers
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
Empty Set :
A set is said to be empty set if it cont no element . The set is denoted by Φ
EVALUATION
CHECKING FOR OPTION : (a)
The set of odd numbers that are divisible by 2
The set of odd numbers are of the form
{ 2n + 1 : n ∈ W }
We know that when we divide 2n + 1 by 2 the remainder is 1
Thus when we divide an odd number by 2 the remainder is 1
So there is no odd number that are divisible by 2
So the set of odd numbers that are not divisible by 2 is empty set
Hence this option is correct
CHECKING FOR OPTION : (b)
The set of prime numbers that are odd numbers
3 , 5 , 7 are examples of prime numbers that are odd numbers
So the set of prime numbers that are odd numbers is not empty
Hence this option is not correct
CHECKING FOR OPTION : (c)
The set of even numbers that are prime numbers
2 is the even number that is prime number
So the set of even numbers that are prime numbers is not empty
Hence this option is not correct
CHECKING FOR OPTION : (d)
The set of multiplies of 3 that are prime numbers
3 is the multiple of 3 that is prime number
So the set of multiplies of 3 that are prime numbers is not empty
Hence this option is not correct
FINAL ANSWER
Hence the correct option is
a. The set of odd numbers that are divisible by 2
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