Question

Use the roster method to write each of the given sets. (Enter EMPTY for the empty set.)

(a) The set of natural numbers x that satisfy x + 4 = 1.
(b) Use set-builder notation to write the following set.
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

Answer 1

a) Empty set

b)
`\{x : x \in N \text{ and } x < 13\}`

Explanation:

Roster form is a comma separated list form of set.

a) The set of natural numbers x that satisfy x + 4 = 1.

`x + 4 = 1\\x = -3 \\otin N`

Thus, x is an empty set.

b) set-builder notation for the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

We use x to represent this set. Now x belongs to natural number and is less than equal to 12.

Thus, it can be written as:

`\{x : x \in N \text{ and } x < 13\}`