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Intro to Geometry

Logic The study of reasoning. Allow us to determine if a statement is true, false, or uncertain.
Open Sentence Contains no truth value. Contains a variable.
3x+2=7 Open Sentence
10+4=15 Closed Sentence
Hannah has blue eyes. Closed Sentence
She has blue eyes. Open Sentence
Negatation (~) place not in the statement or remove it. A statement and it's negatation have opposite truth values.
Conjunction Compound sentence formed by using and. (^) Only true when both parts are true.
Disjunction A compound sentence formed by using or (v) Only false when both parts are false. Only needs at least one true.
Conditional A compound sentence using if....then or implies (➡)
Biconditional (p ➡ q)^(q ➡ p) if and only if or (p ⬅➡ q) True when both parts match.
Hypothesis Follows if
Conclusion Follows then
Consiquent Another word for conclusion
Compound Statement T,F,T,F Sentence that is a mixture of true and false
Tautology Compound sentence that is always going to be true T,T,T,T
Logically Equivalent 2 statements that always have the same truth value. If it is logically equivalent it is tautology.
Law of Detachment R ➡ ~W R ________ ~W
Conditional (original) P ➡ Q
Converse Q ➡ P Switch
Inverse ~P ➡ ~Q Negate
Contrapositive ~Q ➡ ~P Switch and Negate
A conditional and it's contrapositive always have same truth value Logically Equivalent
The converse and its inverse always have the same truth value Logically Equivalent
Law Any thing that is true
Given/ Premise Always true
Modus Tollens A conditional Premise Negation of the Conclusion ____________________________ Conclude Negation of Hypothesis
What is the difference between Law of Detachment and Modus Tollens? In law of deatchment same symbols line up. P➡Q P ______ Q
Modus Tollens= Contrapositive and Law of Detachment
Created by: Naylor