Sets

Empty set is a ___?

• Infinite set

• Finite set

• Unknown set

• Universal set

Answer explanation

The cardinality of the empty set is zero, since it has no elements. Hence, the size of the empty set is zero.

How many elements are there in the complement of set A?

• 0

• 1

• All the elements of A

• None of these

Answer explanation

The complement of a set A will contain the elements that are not present in set A.

The number of elements in the Power set P(S) of the set S = {1,2,3} is:

• 4

• 8

• 2

• None of these

Answer explanation

Number of elements in the set S = 3.

Number of elements in the power set of set S = {1,2,3} = 2³ = 8.

Which of the following two sets are equal?

• A={1,2} and B={1}

• A={1,2,3} and B={2,1,3}

• A={1,2} and B={1,2,3}

• A={1,2,4} and B={1,2,3}

Answer explanation

Two sets are said to be equal if they both have the same elements.

If A, B and C are any three sets, then A × (B U C) is equal to:

• (A × B) U (A × C)

• (A U B) × (A U C)

• (A × B) ∩ (A × C)

• None of these

Answer explanation

Given, A, B and C are any three sets.

Now, A × (B U C) = (A × B) U (A × C).

The set of whole numbers greater than 50 is an infinite set.

• True

• False

Answer explanation

True, because there is infinite number of numbers greater than 50.

The empty set is a subset of every set.

• True

• False

Answer explanation

An empty set contains no elements while a subset contains elements that are not in the other comparing set. Hence, an empty set becomes a subset of all the other sets because it has no elements and the other set contains elements.

Identify whether it is a finite or infinite set.

A = {x : x ∈ N and x is even}

Identify whether it is a finite of infinite set.

G = {The set of letters in the English alphabet}

Identify whether it is a finite or infinite set.

R = The set of fractions with numerator 3.