Question

Which of the following statements are TRUE or False. (Explain why it’s true or false?)

Subtracting a positive number from a negative number always gives you a negative number.

Subtracting two negative numbers always gives you a negative number.

Subtracting a - b is the same as adding a + (-b).

A positive number minus a negative number is always a positive number.

The difference of a number and its opposite gives you zero.

Zero minus a number is the same as a number minus zero.

Answer 1

1) Subtracting a positive number from a negative number always gives you a negative number.

The above statement is true.

Reeason : Let A be a negative number and B be a positive number.

Then, A < 0 and B > 0 ,i.e., -B < 0.

Now, A+(-B) < 0

i.e., A-B < 0

Therefore, subtracting a positive number from a negative number always gives you a negative number.

2) Subtracting two negative numbers always gives you a negative number.

The above statement is false.

Reason : Let A and B be two negative numbers.

Then, A < 0 and B < 0.

If A < B then A-B < 0 ,i.e., A-B is negative.

If A > B then A-B > 0 ,i.e., A-B is positive.

Therefore, subtracting two negative numbers give either positive number or negative number.

3) Subtracting a-b is the same as adding a+(-b).

The above statement is true.

Reason : Let A and B be two numbers.

Let A-B = k

Then, A-B-A = k-A

i.e., -B = k-A

Now, A+(-B) = A+(k-A) = A+k-A = k

i.e., A+(-B) = A-B

Therefore, subtracting a-b is the same as adding a+(-b).

4) A positive number minus a negative number is always a positive number.

The above statement is true.

Reason : Let A be a positive number and B be a negative number.

Then A > 0 and B < 0 ,i.e., -B > 0.

Now, A+(-B) > 0

i.e., A-B > 0

Therefore, a positive number minus a negative number is always a positive number.

5) The difference of a number and its opposite gives you zero.

The above statement is false.

Reason : Let A be a number.

Then its opposite number is 1/A.

Now, A-(1/A) may be negative or zero or positive.

It is zero only for A = 1.

6) Zero minus a number is the same as a number minus zero.

The above statement is false.

Reason : Let A be a number.

Let A-0 = k.

Then, A = k.

Now, 0-A = -A = -k.

Therefore, A-0 is not equal to 0-A.