Question

Use the definition of less than to show each of the following:

a. 2 < 4

b. 3 < 100

c. 0 < 3

Answer 1

I would show on a number line that the less than number is always to the left of the other number.

Answer 2

[AI-generated answer — Explain Bot]

To show each of the following using the definition of less than:

a. 2 < 4:

The definition of less than states that a < b if b - a is a positive number. In this case, we subtract 2 from 4:

4 - 2 = 2

Since the result is a positive number (2), we can conclude that 2 is less than 4. Therefore, 2 < 4 is true.

b. 3 < 100:

Similarly, we can apply the definition of less than by subtracting 3 from 100:

100 - 3 = 97

Since the result (97) is positive, we can conclude that 3 is less than 100. Therefore, 3 < 100 is true.

c. 0 < 3:

In this case, we subtract 0 from 3:

3 - 0 = 3

Since the result is positive (3), we can conclude that 0 is less than 3. Hence, 0 < 3 is true.