Chapter 0.CT, Problem 1CT

To determine

To list:

The odd integers from the set $\left\{-7,-\frac{2}{3},0,1,3,\sqrt{10},4\right\}$.

Answer to Problem 1CT

Solution:

$-7,1,3$

Explanation of Solution

Approach:

1) A set is a collection of objects.

2) The numbers that we use for counting are called natural numbers. The collection of natural numbers is denoted by N and is written as $N=\{1,2,3,\mathrm{4....5},\mathrm{...125...}\}$.

3) If 0 is included in the collection of natural number these numbers are called whole numbers.

The collection of whole numbers is denoted by W and is written as $W=\{0,1,2,3,\mathrm{4....5},\mathrm{...125...}\}$.

4) The set of whole numbers and their negatives are called integers and denoted by Z and written as $Z=\{\mathrm{...}-3,-2,-1,0,1,2,\mathrm{3...}\}$.

5) Even and odd integers are subsets of integers.

6) Even integers are exactly divisible by 2. The set of even integers is $\{\mathrm{...10},-8,-\mathrm{6...0},2,4,\mathrm{6...}\}$.

7) Odd integers are not exactly divisible by 2. The set of odd integers is $\{\mathrm{...9},-7,-\mathrm{5...0},3,5,\mathrm{7...}\}$.

Calculation:

Consider the set $\left\{-7,-\frac{2}{3},0,1,3,\sqrt{10},4\right\}$.

-7, 1 & 3 are the only odd integers amongst the numbers given in the set.