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AysviL [449]
3 years ago
9

Select True or False for each statement.

Mathematics
2 answers:
mote1985 [20]3 years ago
7 0
<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 a, so it is true that:

a+0=a

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

This is false, because:

a+(-a)=a-a=0

For any number a there exists a number -a such that a+(-a)=0

  • 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:

\mid a-b \mid= \mid b-a \mid

  • 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:

(a + b)(a + c)=a^2+ac+ab+bc \\ \\ a^2+ab+ac+bc \neq a+(b.c)

  • 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:

\frac{u}{v} \\ \\ v \neq 0

Given that a \ and \ b are rational, then the result of dividing them is also a rational number.

prohojiy [21]3 years ago
3 0

Answer:

A) True

B) False

C) True

D) False

E) True

Step-by-step explanation:

We are given the following statements in the question:

A) True

For  every real number, a, a + 0 = a. 0 is known as the additive identity.

B) False

For a real number a, a + (-a) = 0.

C) True

For a real numbers a and b, |a-b| = |b-a|

D) False

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

Counter example: For a = 2, b =  1, c = 3

a + (b.c) = (a + b)(a + c)\\2 + (1.3) \neq (2+1)(2+3)\\5\neq 15

E) True

For rational numbers a and b, b is not equal to zero, \frac{a}{b} is always a rational number.

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