This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “The Empty Set”.

1. Find the odd one out.

a) Null set

b) Void set

c) Infinite set

d) Empty set

View Answer

Explanation: Null set, void set, or empty set is a set which contains no elements. Infinite set is a set having infinite number of elements.

2. Which of the following is representation of empty set?

a) ( )

b) [ ]

c) { }

d) < >

View Answer

Explanation: Empty set is a set which does not contain any element. It can be represented by { } or ϕ symbol.

3. Which of the following is an empty set?

a) Prime numbers up to 10

b) Even numbers up to 10

c) Prime numbers divisible by 2

d) Prime numbers divisible by 3

View Answer

Explanation: Prime number is a number which is only divisible by 1 and itself. So, there is no prime number divisible by 3. So, it is an empty set.

Set of prime numbers up to 10 is {2,3,5,7} Set of even numbers up to 10 is {2,4,6,8} Set of prime numbers divisible by 2 is {2}.

4. Find the number of points common to parallel lines.

a) Three points

b) One point

c) Two point

d) No point

View Answer

Explanation: Since parallel lines do not intersect anywhere they do not have any point in common. So, no point is common to parallel lines.

5. Is set {x : x is a natural number x<5 and x>7} a null set?

a) True

b) False

View Answer

Explanation: A number less than 5 cannot be greater than 7. If we plot points less than 5 on the number line and then plot numbers greater than 7 on it we find, no point is common to both so, it is a null set.

6. Which of the following is a null set?

a) {x : x is a natural number and x^{2}=4}

b) {x : x is a rational number and x^{2}=2}

c) {x : x is an even prime number}

d) {x : x is name of the day of week}

View Answer

Explanation: x

^{2}=4 => x=2,-2 where 2 is a natural number so X={2}.

X={2} for even prime number. Also we have seven days of the week so they cannot form null set.

x

^{2}=2 => x=√2, -√2 they both are irrational so, it is a null set.

7. The number of elements in a null set is ______________

a) zero

b) one

c) two

d) any

View Answer

Explanation: Null set or empty set is a set which does not contain any element. So, the number of elements in a null set is zero.

8. Find the solution to set {x : x is a natural number and 2x+1=2}.

a) {1}

b) {2}

c) {1/2}

d) { }

View Answer

Explanation: 2x+1=2 => 2x = 1

x=1/2 which is not a natural number. So, the solution to given set is { }.

9. A set with no elements in it is called?

a) Equivalent Set

b) Empty Set

c) Equal Set

d) Infinite Set

View Answer

Explanation: An empty set is a set which contains 0 elements and is denoted by {}.

10. Which of the following is an empty set?

a) The set of dogs with six legs

b) The set of books in the library

c) The set of boys in a school

d) The set of a square with 4 sides

View Answer

Explanation: Clearly there is no dog in this world with 6 legs hence this makes an empty set.

11. If B is a null set and A is some set then which one of the following is false?

a) B⊆A

b) B∪A=A

c) B∩A=A

d) B∩A=B

View Answer

Explanation: An empty set is a subset of every set, also the union of a set with an empty set gives the set itself, Since, there are no elements in an empty set hence intersection with an empty set gives empty set.

12. The subset of a null set is the null set itself.

a) True

b) False

View Answer

Explanation: The null set has no elements to form a subset hence its subset is a null set itself.

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