Chapter 1.CM, Problem 1CM

To determine

To find:

The even integers from the given set $\left\{-5,-3,-2,0,1,\sqrt{2},2,\frac{5}{2},5,6,11\right\}$.

Answer to Problem 1CM

Solution:

The even integers are $\left\{-2,0,2,6\right\}$.

Explanation of Solution

Natural Numbers:

Natural numbers also called counting numbers are the whole numbers greater than zero.

The natural numbers do not include the negative numbers.

For example, $1,2,3,4,\dots$

Integers:

All positive and negative whole numbers are called integers and also include zero.

For example, $\dots ,-4,-3,-2,-1,0,1,2,3,4,\dots$

Prime Numbers:

Prime numbers are numbers greater than one and divisible by its own. For example, $2,3,5,7,11,13,17,\dots$ are prime numbers.

Calculation:

Given:

$\left\{-5,-3,-2,0,1,\sqrt{2},2,\frac{5}{2},5,6,11\right\}$.

From the given set, using above definition we find that the integers are

$\left\{-5,-3,-2,0,1,2,5,6,11\right\}$

From the above set, we find that the even integers are $\left\{-2,0,2,6\right\}$.

Final statement:

The even integers are $\left\{-2,0,2,6\right\}$.