Test: Sets - ACT MCQ

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

The cardinality of the power set is equal to 2ⁿ, where n is the number of elements in a given set.

Given,
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
P = {1, 2, 5}
Q = {6, 7}
Q’ = {1, 2, 3, 4, 5, 8, 9, 10}
Hence,
P ∩ Q’ = {1, 2, 5} = P

Given,
X = {1, 4, 9, 16, 25,…}
X = {12, 22, 32, 42, 52, …}
Therefore,
X = {x: x is a set of square numbers}

Let the given function be
y = 3x – 2
⇒ y + 2 = 3x
⇒ x = (y + 2)/3
Since, for all values of y, x has different values. Thus, values of x and y can range from -∞ to ∞.
So, Range{f(x)} = R = (-∞, ∞).

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

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

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

Given,
Set X = {x: x∈N, x≤10}
X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Number of elements of power set of X, P(X) = 210 = 1024

Given,
A, B and C are any three sets.
Now, A × (B ∪ C) = (A × B) ∪ (A × C)