Question

Select True or False for each statement.

1. For a real number a, a + 0 = a.

2. For a real number a, a + (-a) = 1.

3. For a real numbers a and bla-bl=1b-al.

4. For real numbers a, b, and c, a +(bº c) = (a + b)(a + c).

5. For rational numbers a and b when b# o,
is always a rational number.

Answer 1

1. True
2. False
3. True
4.true

Answer 2

1. True

2. False

3. True

4. False

5. True

Explanation:

1. For a real number a, a + 0 = a.

This is true, any number plus zero is that number.

2. For a real number a, a + (-a) = 1.

This is false. Adding a negative number is the same as subtracting that number. So a + (-a) = a - a = 0

3. For a real numbers a and b la-bl = |b-al.

This is true. Absolute value represents the distance between two numbers. This number can never be negative, therefore la-bl = |b-al.

4. For real numbers a, b, and c, a +(bº c) = (a + b)(a + c).

False. a + (b * c) = a + bc.

If you foil (a + b)(a + c) you will see its equal to a²+ab+ac+bc, which is definitely different than a + (b*c)

5. For rational numbers a and b when b# o, is always a rational number.

True, a rational number is one that can be written as a fraction with two integers. The quotient of two rational numbers can always be written as a fraction with integers.