Logic is:

• the study of critical thinking or reasoning
• an organized systematic approach to establishing proof or validity

Reasoning is the ability:

• to reach conclusions by a systematic comparison of facts
• to perform the process of deduction or of induction
• to formulate and set forth propositions and the inferences from which to prove and argue

Reasoning relies on the order of the sentences or statements being put together. The letters "p" and "q" represent parts of the mathematical statements.

The truth value is:

• the determination that a mathematical statement is true or false
• a determination of "true" or "false" is assigned to a single statement

• A triangle has three sides. Is that a true or false statement?
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  true
• A triangle has four angles. Is that a true or false statement?
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  false

Validity is:

• a determination of truth based on the comparison of, or relationship between two or more statements
• a logically valid statement is one where the conclusion (q) supports the hypothesis (p)
• an invalid argument is where the conclusion does not support the hypothesis

• is dependent on establishing related conditional statements truth value
• a Conditional Statement is true if the hypothesis is true and the conclusion that follows is also true
• a Conditional Statement is false ONLY when the hypothesis is true but the conclusion is false.

Example: If an integer is even, then it is divisible by four (no remainder).

Give an example showing the validity of the statement.

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6 does not work: 6 4 = 1 with a remainder of 2

(For a conditional statement to be true, the hypothesis has to be a subset of the conclusion.)

Therefore the conditional Statement is FALSE because the conclusion does not work for all elements of the hypothesis and the hypothesis is true.

A counter example is an example that doesn't work for, solve, or match the description of the statement. Counter means "against;" meaning finding something that challenges the truth of a statement.

Find counter examples for the following statements:

1. All horror movies have vampires in them. Click here for a possible counter example. Night of the Living Dead (about zombies)
2. All roses are red. Click here for a possible counter example. Yellow roses exist.
3. All birds can fly. Click here for a possible counter example. The ostrich can't fly and it is a bird.
4. All prime numbers are odd numbers. Click here for a possible counter example. "2" is ia prime number and it is even.

A statement is either true or false, but not both.

Are the following statements true or false? If the statement is false, provide a counter example to support your decision.

1. George Washington was the first president of the United States. Click here to check your answer. True
2. A negative integer times a negative integer produces a negative result. Click here to check your answer. -2*-2=+4
3. All perfect square numbers are positive. Click here to check your answer. True
4. Any three points are coplanar. Click here to check your answer. True
5. The measure of an obtuse angle is less than 90 degrees. Click here to check your answer. False

Essentially, when a statement is true or false, you are validating it as true or false by providing reasons for your conclusion.