Describe the following sets in set-builder form: A = 1, 2, 3, 4, … - Vidyadip

Question

Describe the following sets in set-builder form:
A = {1, 2, 3, 4, 5, 6}

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Answer

In set Builder form, a set is described by some characterising property P (x) of its elements x. In this case a set can be described as {x : P (x)hold} which is read as 'the set of all x such that P (x) holds'. The symbols $\because$ or 'I' is read as 'such that'. So the above set A in Set-Builder form may be written as $\text{A} = \{\text{x} \in\text{ N}:\text{x} < 7\}$ i .e A is the set of natural numbers x such that x is less than 7.

Or

$\text{A} = \{\text{x} \in\text{N } | 1 < \text{x} < 6\},$

i.e. A is the set of natural numbers x such that x is greater than or equal 1 and less than or equal to 6.

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