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<h2>Answer:</h2>
For a real number a, a + 0 = a. TRUE
For a real number a, a + (-a) = 1. FALSE
For a real numbers a and b, | a - b | = | b - a |. TRUE
For real numbers a, b, and c, a + (b ∙ c) = (a + b)(a + c). FALSE
For rational numbers a and b when b ≠ 0, is always a rational number. TRUE
<h2>Explanation:</h2>- <u>For a real number a, a + 0 = a. </u><u>TRUE</u>
This comes from the identity property for addition that tells us that<em> zero added to any number is the number itself. </em>So the number in this case is , so it is true that:
- For a real number a, a + (-a) = 1. FALSE
This is false, because:
For any number there exists a number
such that
- For a real numbers a and b, | a - b | = | b - a |. TRUE
This is a property of absolute value. The absolute value means remove the negative for the number, so it is true that:
- For real numbers a, b, and c, a + (b ∙ c) = (a + b)(a + c). FALSE
This is false. By using distributive property we get that:
- For rational numbers a and b when b ≠ 0, is always a rational number. TRUE
A rational number is a number made by two integers and written in the form:
Given that are rational, then the result of dividing them is also a rational number.