Question

Write the formal descriptions of the following sets: (a) The set containing the numbers 5, 9, and 27. (b) The set that contains all the natural numbers less than 2. (c) The set containing the empty string. (d) The set containing nothing at all.

Answer 1

Answer: a)
`=\left \{ 5,\,9,\,27 \right \}`

(b)
`\left \{ x\ : X\varepsilon\mathbb{N} \right \text{and}\ x<2\}= \left \{1 \right \}`

(c)
`\left \{\epsilon \right \}`

(d)
`\left \{\right \}=\phi`

Step-by-step explanation:

The formal description of the given sets are as follows :-

a) The set containing the numbers 5, 9, and 27.

`=\left \{ 5,\,9,\,27 \right \}`

(b) The set that contains all the natural numbers less than 2.

`\left \{ x\ : X\varepsilon\mathbb{N} \right \text{and}\ x<2\}= \left \{1 \right \}`

(c) The set containing the empty string.

We know that in formal description, the empty string is denoted with
`\epsilon`.

Thus, the required set :
`\left \{\epsilon \right \}`

(d) The set containing nothing at all.

`\left \{ \right \}=\phi`