Describing Mathematical System

What do you call the statements that can only be described and not defined?

• axioms

• defined terms

• theorems

• undefined terms

Which of the following is a commutative axiom?

• 2 + 3 = 2 + 3

• 2 + 3 = 3 + 2

• 2 ∙ 3 = 2 ∙ 3

• (2 + 3) = 2(3) + 3(2)

Which statement is NOT true?

• Integers are rational numbers.

• Rational numbers are also irrational.

• All counting numbers are real numbers.

• Numbers from zero to ten are natural numbers.

What is the additive inverse of a = 0?

• 0

• 1 / a

• - a

• - 1 / a

Which of the following illustrates Multiplicative axiom?

• if 𝑎 = 𝑏, then 𝑏 = 𝑎

• if 𝑎 = 𝑏, then

  𝑎 + 𝑐 = 𝑏 + 𝑐

• if 𝑎 = 𝑏 and 𝑏 = 𝑐, then 𝑎 = 𝑐

• if 𝑎 = 𝑏, then,

  𝑎 ∙ 𝑐 = 𝑏 ∙ 𝑐

Which of the following DO NOT imply associative axiom?

• 11 * (5/6) = (5/6) * 11

• [(−2)(6)]8 =

  −2 [(6)(8)]

• (−5 + 7) + 4 =

  −5 + (7 + 4)

• 𝐴 ∙ ( 𝐵 ∙ 𝐶 ) =

  ( 𝐴 ∙ 𝐶 ) ∙ 𝐵

Name the property which justifies the following conclusion.

Given: If 5𝑥 – 5 = 10

Conclusion: then 5𝑥 = 15

• Existence of Additive Inverse.

• Existence of Multiplicative Inverse.

• Existence of Multiplicative Identity.

• Existence of Additive Inverse and Additive Identity.

Which of the following is NOT a property of Mathematical system?

• conjecture

• define terms

• postulates

• theorems

Which of the following statements is true about defined terms?

• These are concepts that need to be defined.

• These are statements accepted after it is proved deductively.

• These are concepts that can be defined using the undefined terms.

• These are statements assumed to be true and need no further proof.

Which of the following statements describes an axiom?

• A statement that is never accepted to be true.

• A statement that is accepted as true without a formal proof.

• A statement that is only accepted as true after being formally proven.

• A statement that is usually not obvious as true, using other rules

  and reasoning.