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- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/02%3A_Logical_Reasoning/2.01%3A_Statements_and_Logical_OperatorsSome mathematical results are stated in the form “P if and only if Q” or “P is necessary and sufficient for Q.” An example would be, “A triangle is equilateral if and only if its three...Some mathematical results are stated in the form “P if and only if Q” or “P is necessary and sufficient for Q.” An example would be, “A triangle is equilateral if and only if its three interior angles are congruent.” The symbolic form for the biconditional statement “P if and only if Q” is P↔Q.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/A_Spiral_Workbook_for_Discrete_Mathematics_(Kwong)/02%3A_Logic/2.01%3A_PropositionsThe rules of logic allow us to distinguish between valid and invalid arguments. Besides mathematics, logic has numerous applications in computer science, including the design of computer circuits and ...The rules of logic allow us to distinguish between valid and invalid arguments. Besides mathematics, logic has numerous applications in computer science, including the design of computer circuits and the construction of computer programs. To analyze whether a certain argument is valid, we first extract its syntax.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_(Levin)/3%3A_Symbolic_Logic_and_Proofs/3.1%3A_Propositional_LogicA proposition is simply a statement. Propositional logic studies the ways statements can interact with each other. It is important to remember that propositional logic does not really care about the c...A proposition is simply a statement. Propositional logic studies the ways statements can interact with each other. It is important to remember that propositional logic does not really care about the content of the statements. For example, in terms of propositional logic, the claims, “if the moon is made of cheese then basketballs are round,” and “if spiders have eight legs then Sam walks with a limp” are exactly the same. They are both implications.
- https://math.libretexts.org/Courses/Saint_Mary's_College_Notre_Dame_IN/SMC%3A_MATH_339_-_Discrete_Mathematics_(Rohatgi)/Text/3%3A_Symbolic_Logic_and_Proofs/3.2%3A_Propositional_LogicA proposition is simply a statement. Propositional logic studies the ways statements can interact with each other. It is important to remember that propositional logic does not really care about the c...A proposition is simply a statement. Propositional logic studies the ways statements can interact with each other. It is important to remember that propositional logic does not really care about the content of the statements. For example, in terms of propositional logic, the claims, “if the moon is made of cheese then basketballs are round,” and “if spiders have eight legs then Sam walks with a limp” are exactly the same. They are both implications.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_220_Discrete_Math/2%3A_Logic/2.1%3A_PropositionsThe claim is true if A is a real number, but it is not always true if A is a matrix 1 . Thus, it is not a proposition. The result is called the negation of p, and is denoted ∼p or ...The claim is true if A is a real number, but it is not always true if A is a matrix 1 . Thus, it is not a proposition. The result is called the negation of p, and is denoted ∼p or ¬p, both of which are pronounced as “not p.” The similarity between the notations ∼p and −x is obvious. We can also write the negation of p as ¯p, which is pronounced as “p bar.” The truth value of ¯p is opposite of that of p.
- https://math.libretexts.org/Courses/Borough_of_Manhattan_Community_College/MAT_310_Bridge_to_Advanced_Mathematics/02%3A_Logic/2.04%3A_Truth_Tables_for_StatementsThe statement (P∨Q)∧∼(P∧Q), contains the individual statements (P∨Q) and (P∧Q), so we next tally their truth values in the third and fourth columns. This...The statement (P∨Q)∧∼(P∧Q), contains the individual statements (P∨Q) and (P∧Q), so we next tally their truth values in the third and fourth columns. This truth table tells us that (P∨Q)∧∼(P∧Q) is true precisely when one but not both of P and Q are true, so it has the meaning we intended. (Notice that the middle three columns of our truth table are just "helper columns" and are not necessary parts of the table.
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/02%3A_Logical_Reasoning/2.01%3A_Statements_and_Logical_OperatorsSome mathematical results are stated in the form “P if and only if Q” or “P is necessary and sufficient for Q.” An example would be, “A triangle is equilateral if and only if its three...Some mathematical results are stated in the form “P if and only if Q” or “P is necessary and sufficient for Q.” An example would be, “A triangle is equilateral if and only if its three interior angles are congruent.” The symbolic form for the biconditional statement “P if and only if Q” is P↔Q.
