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  2. PRINCIPLES OF LOGIC (quiz no.1) Flashcards | Quizlet

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    The proposition (p & q) is true if both p is true and q is true; it is false if either p is false or q is false (or both): (T & T) = T, (T & F) = F, (F & T) = F, (F & F) = F . The operation & is sometimes represented by a wedge (∧) or the word "and." Here is the truth table for & :
    In logic, the proposition (p → q) is true whenever p is false, which some people find counter-intuitive. In fact, that (F → T) and (F → F) are both true is a matter of definition, but the definition does not disagree with common usage: Think of (p → q) as the assertion (if p then q), that is, "if p is true, then q is also true."
    That is, p and q are logically equivalent if p is true whenever q is true, and vice versa, and if p is false whenever q is false, and vice versa. If p and q are logically equivalent, we write p = q . Logical operations act on propositions, turning them into other propositions.
    A proposition p is a statement that can be true (T) or false (F). Logical operations turn propositions into other propositions; examples include !, |, &, →, ↔. They operate as shown in the following table: The logical operations satisfy associative, commutative, and distributive laws. | is like addition and & is like multiplication.
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