Inductive Reasoning= a type of reasoning that reaches conclusions based on a pattern of specific examples or past events
Conditional= if->then statements
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