Geometry Logic and Reasoning

Inductive reasoning

drawing conclusions based on examples

Conjecture

an "educated guess", a rule based on a pattern, but it is not proven to be true.

Counterexample

an example that proves that a conjecture or statement is false

deductive reasoning: LOGIC

Using facts, true statements, and logic to reach a true statement or conclusion.

conditional statement

a statement that can be written in “if-then” form

Hypothesis

The part of an if-then statement right after the word "if".

Conclusion

The part of an if-then statement right after the word "then".

negation

the opposite of the original statement

converse statement

A statement made by swapping the "if" and "then" parts (If q, then p) For example, the converse of "If it rains, then the ground is wet" is "If the ground is wet, then it rains."

Inverse statement

Made by adding "not" to both the "if" and "then" parts (If not p, then not q) For example, the inverse of "If it rains, then the ground is wet" is "If it does not rain, then the ground is not wet."

Contrapositive

Made by swapping and adding "not" to both parts (If not q, then not p). For example the contrapositive of "If it rains, then the ground is wet" is "If the ground is not wet, then it does not rain."

biconditional statement

When the conditional statement and its converse are both true then you can make it as only one "if and only if" (iff) statement.

Conjunction

two or more statements joined together with the word “and”

Disjunction

two statements joined with the word “or” to form a compound statement.

Law of Detachment

If a conditional is true and its hypothesis is true, then its conclusion is true.

Law of Syllogism

If p-->q and q-->r are true statements, then p-->r is a true statement.

Law of Contrapositive

if a conditional statement is true then the contrapositive is true

Converse Error

A mistake in logic where you wrongly assume that because the "then" part is true, the "if" part must be true. If p is true then q is true. q is true. Therefore, p is true.

Inverse Error

A mistake in logic where you wrongly assume that because the "if" part is false, the "then" part must be false. If p is true then q is true. ~P is true. Therefore, ~q is true.