Inductive Reasoning= a type of reasoning that reaches conclusions based on a pattern of specific examples or past events

Conditional= if->then statements

If= hypothesis

Then= conclusion

P= abbreviation for hypothesis

Q= abbreviation for conclusion

P->Q= read as “p implies q”

Counterexample= an example showing that a statement is false

Venn Diagram= can be used to illustrate a conditional

“True” & “False”= truth values

Converse= hypothesis and conclusion of the conditional are flipped/exchanged(if q, then p)

Inverse= negate the conditional (if NOT p, then NOT q)

Contrapositive= negate the converse (if not q, then not p)

Biconditional= joining the conditional and the converse with the words if and only if

Iff= abbreviation for “if and only if”

Deductive Reasoning= reasoning based on fcat

In geometry, we use definitions, postulates, theorums, and given information to support the statements we make.

Law of Detachment= IF the hypothesis of a true conditional is true, then the conclusion is true. Example: If a vehicle is a car, then it has four wheels. A sedan is a car. Conclusion based on Law of Detachment: A sedan has four wheels.

Rule for Law of Detachment= if even one counterexample can be provided against the conclusion created, there is not correct conclusion.

Law if Syllogism= if p->q is true, and q->r is true, then p->r is true. With this law, you are basically leaping over the “q” to reach a conclusion. Example: If you are a careful driver, then you do not text while driving. (p= you are a careful driver & q= you do not text while driving) If you do not text while driving, then you will have fewer accidents. (q= you do not text while driving & r= you will have fewer accidents)

Conclusion= If you are a careful driver, then you will have fewer accidents. (p->r)

Addition Property of Equality= if a = b, then a + c = b + c

Subtraction