Summary of chapter 1 on discrete mathematics

[Sarah111-AHM]

• Logic is important for understanding and constructing correct mathematical arguments.
• A proposition is a declarative sentence that is either true or false, but not both.
• Propositional variables are denoted by letters such as p, q, r, and s.
• A proposition is a declarative sentence that is either true or false.
• The negation of a proposition, denoted by ¬p, is the statement "It is not the case that p."
• The truth value of the negation of p, ¬p, is the opposite of the truth value of p.
• The conjunction of two propositions p and q, denoted by p ∧ q, is the proposition "p and q."
• The conjunction p ∧ q is true when both p and q are true, and false otherwise.
• The disjunction of two propositions p and q, denoted by p ∨ q, is the proposition "p or q."
• The disjunction p ∨ q is false only when both p and q are false.
• Truth tables can be used to show the possible truth values of logical expressions.