Question

Which of the following is an empty set?

Answer 1

Answer:

In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced.

Answer 2

SOLUTION

COMPLETE QUESTION

Which of the following is 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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