Give an example of an empty set. and Explain why it is empty.
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Empty Set.
If there is no element in a set, then that set is called an Empty Set. This set is also called Null Set or Void Set. We denote an Empty Set by Greek letter Φ or two closed second brackets that is { }.
- Null set has no subset because its only subset is it itself.
- It also has no proper subset because no set can be its own proper subset.
Example:
- We know 'man is mortal', the the set of 'immortal men' is an Empty Set.
- A = {x : x is an integer and 5 < x < 6} is an Empty Set because there is no integer in that region.
- B = {x : x is a prime number and 14 ≤ x ≤ 16} is an Empty Set because there is no prime number in that region.
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