What Is A Mathematical Statement & What Is Logic?

In This Post, You Will Learn What A Mathematical Statement Is, Types Od Mathematical Statements, & What Logic Is.

*One of the goals of studying mathematics is to develop the ability to think critically. The study of critical thinking, or reasoning, is called logic.

*All reasoning is based on the ways we put sentences together. A mathematical sentence is a sentence that states a fact & can be judged to be true or false.

-Questions and phrases are not mathematical sentences since they cannot be judged to be true or false.

Ex:"An isosceles triangle has two congruent sides." is a true mathematical sentence.

There are two types of mathematical sentences:

An open sentence is a sentence which contains a variable.

• "x + 2 = 8" is an open sentence -- the variable is "x."
• "It is my favorite color." is an open sentence-- the variable is "It."

• A closed sentence, or statement, is a mathematical sentence which can be judged to be true or false. A closed sentence, or statement, has no variables.

• "Garfield is a cartoon character." is a true closed sentence, or statement.
• "A pentagon has exactly 4 sides." is a false closed sentence, or statement.
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In logic, a conjunction is a compound sentence formed by combining two sentences (or facts) using the word "and." A conjunction is true only when BOTH sentences (or facts) are true.

Examples:

- "Blue is a color and 7 + 3 = 10." (T and T = T)
Since both facts are true, the entire sentence is true.

-"One hour = exactly 55 minutes and one minute = exactly 60 seconds."
(F and T = F) Since the first fact is false, the entire sentence is false.

And lastly, Sentences, or statements, that have the same truth value are logically equivalent.

Great! Now Identify Which Problems Are Mathemathical Statements & Whether They Are True Or False:

1. 7+8.

2. A square has the same amount of sides as a circle.

3. All triangles have angle relationships.

Sources: http://regentsprep.org/regents/math/geometry/GP1/sentence.htm

http://regentsprep.org/regents/math/geometry/GP1/conjunct.htm