Question

Let the universal set be the set of integers and let A = x^2 ≤ 5. Write A using the roster method.

A = { } --use commas to separate elements in the set

*Finite Math question

Answer 1

The set A = x^2 ≤ 5, which includes all integers whose squares are less than or equal to 5, is expressed using the roster method as A = { -2, -1, 0, 1, 2 }.

Step-by-step explanation:

The set A includes all integers x such that x squared is less than or equal to 5. To list the set using the roster method, we identify all integers which, when squared, give a result that does not exceed 5.

The integers satisfying x2 ≤ 5 are -2, -1, 0, 1, and 2 because:

• (-2)2 = 4, which is less than or equal to 5,
• (-1)2 = 1, which is less than or equal to 5,
• 02 = 0, which is less than or equal to 5,
• 12 = 1, which is less than or equal to 5,
• (2)2 = 4, which is less than or equal to 5.

Therefore, using the roster method, the set A is written as A = { -2, -1, 0, 1, 2 }.

Answer 2

Step-by-step explanation:

Given that Z the set of integers is the universal set and

A is given in set builder form.

`A = x`

To convert this into roster form, we can find solutions for x

When
`x^2\leq 5\\|x|\leq √(5) =2.236`

i.e. all integers lying between -2.236 and 2.236

The only integers satisfying this conditions are

-2,-1,0,1,2

Hence A in roster form is

A=
`{-2,-1,0,1,2}`