Empty Set

A set that contains no elements is called an empty set, null set, or void set. It is denoted by ϕ or {}.

(i) A = {x : x is a natural number smaller than 1}

(ii) D = {x : x is a odd number divisible by 2}

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1. Set A: A = {x |x is a natural number smaller than 1}

• The smallest natural number is 1, so there is no natural number smaller than .

- Thus, A is an empty set because it has no123 elements.

2. Set D: D = {x |x is an odd number divide by 2}

- An odd number is never divisible by .

- Hence, D is an empty set because no510100 such number exists.

• ϕ (empty set) and {0} (set containing 0) are different.

• ϕ = {} → A set with no1001000 elements.

- {0} → A set that contains one element, which is .

Thus, the empty set has no elements, while {0} contains the number 0 as an element.