logic and proof 1

• logic is a study of reasoning, specifically concerned with whether reasoning is correct
• logic is used to prove theorems in mathematics
• logic focuses on the relationship among statements as opposed to the content of any particular statement
• world is made up of objects and that objects can be organized to form collections
• Statements describing the world can be true/false
• A statement is a description of something
• a proposition is a declarative statement (that is, a sentence that declares fact) that is either true or false but not both.
• according to the law of the excluded middle: a proposition cannot be partially true or partially false
• according to the law of contradiction: a proposition cannot be both true and false
• a statement is not a proposition if the it is asking question, commanding, or there is an unknown value (for mathematical equations)
• in order to formalize logic, we need a system for translating statements into symbols
• in propositional logic, we assume a combination/ collection of propositions are given as p, q, r, or s which is called proposition variables
• we form compound propositions by using logical connectives(logical operators) to form propositional "molecules"