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MA100 Lecture Notes - Contraposition, Prime Number, If And Only If

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scarletcricket964

16 Oct 2011

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Document Summary

In mathematics a statement is a declarative sentence that can be true or false but not both. A mathematical identity is an equality relation that is always true for all values of the variable in the relation. Ex. (x+3)2 = x2 + 6x + 9 ex. An equation is an equality relation depending on some variables for which we are asked to find all values that make the statement true. Clearly not an identity since for x=0 -6=0. X= 6 you can always check by substituting. I think therefore i am if a triangle is equilateral then all interior angles are 60 . Prove that if m and n are even numbers then m+n is also even. The converse of a statement is a statement obtained by switching the hypothesis with the conclusion. If a statement is true it is not always guaranteed that its converse is true.

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Related Questions

Equations and Inequalities

Equations: True or False?

Independent Practice

1. Consider the statement: 4 - 3 + 5 = -6 + 8 + 4. This is a mathematically correct sentence.

Is the sentence true or false? Explain how you know.

2. Determine if the sentence is true. Select all that apply.

3. Determine whether the following number sentences are TRUE or FALSE. Justify your answer.

4. For the equation, x-7=24, can a value be substituted for x to make that a true number sentence? How many values could be substituted for x and have a true number sentence?

5. Consider x+4=x+8 . What values could be substituted for x to make this a true number sentence? Explain how you know.

6. Determine what value(s) for the variable would make each algebraic equation a true number sentence.

is true for _______________.

is true for _______________.

is true for _______________.

7. Which of the following has the correct solution given for x? Check all that apply.

In the following exercises, use the Intermediate Value Theorem (IVT).

Use the statement "The cosine of t is equal to t cubed."

a. Write a mathematical equation of the statement.

b. Prove that the equation in part a. has at least one real solution.

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