Empty Set Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Decide which are true: (a) ∅={0}\emptyset = \{0\}, (b) ∅⊆{1,2,3}\emptyset \subseteq \{1,2,3\}, (c) ∣∅∣=0|\emptyset| = 0.

Solution

  1. 1
    (a) False. ∅\emptyset has no elements; {0}\{0\} has one element (zero). They are different sets.
  2. 2
    (b) True. The empty set is a subset of every set.

Answer

(a)  False,(b)  True,(c)  True(a)\;\text{False},\quad (b)\;\text{True},\quad (c)\;\text{True}
The empty set has zero elements, so its cardinality is 0. It is a subset of every set but not equal to any non-empty set.

About Empty Set

The empty set, denoted ∅\emptyset or {}\{\}, is the unique set that contains no elements at all. It is a subset of every set because the statement 'every element of ∅\emptyset belongs to AA' is vacuously true — there are no elements to contradict it.

Learn more about Empty Set →

More Empty Set Examples

Example 1 easy

Determine whether each set is empty: (a) [formula], (b) [formula], (c) [formula].

Example 2 medium

Prove that the empty set [formula] is a subset of every set [formula].

Example 4 medium

Let [formula]. Find: (a) [formula] for any set [formula], (b) [formula] for any set [formula], (c) [

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Related Concepts

SetCardinality