Geometry Unit 2

Or Rule

p or q is a true statement. If ~p is true, then q is true. If ~q is true, then p is true.

Conjunction

∩ Intersection - and

Disjunction

U Union - or

Law of Contrapositive

If p → q is a true conditional statement, then ~q → ~p is a true statement.

Law of Syllogism

If p → q and q → r are true conditional statements, then p → r is true.

Inverse Error

If p → q then ~p → ~q is not valid.

Converse Error

If p → q then q → p is not valid.

Law of Detachment

If p → q is a true conditional statement and p is true, then q is true.

Venn diagram

the little circle inside the big circle is the hypothesis, and the big circle is the conclusion

only if equivalent

then

Converse

q → p

Inductive reasoning

Specific - general

Hypothesis and conclusion

Hypothesis = "if" part, and is represented by a red "p", conclusion = "then" part, is represented by a blue "q"

Conjecture

A generalization based on observed facts

Deductive reasoning

General - specific

Contrapositive

~q → ~p

Biconditional statement

A statement that is written in the "if and only if" form, and is true in both the conditional and converse.

Conditional statement

a statement written in the "if-then" form p → q

Counter example

An example that proves a statement false

Inverse

~p → ~q