Logic Flashcards
is the study of methods of reasoning or argumentation. It is also a science or study of how to evaluate arguments and reasoning.
Logic
is a declarative sentence which is true or false, but not both.
proposition or statement
one and only one of which is assignable to any given statement is called the
‘truth value’ of that statement.
are used to represent propositions, usually denoted by small letters, such as p, q, r, s and t.
Propositional variables
contains one or more variables, that is, it is either true or false depending on the value of the placeholder.
open sentence
on the other hand, is a mathematical sentence that is known to be either true or false.
closed sentence
is a proposition formed from simple propositions using logical connectors or some combinations of logical connectors.
compound proposition
are words, expressions, or phrases that point out the number of elements that a statement relates to
Quantifiers
There are two types of quantifiers:
universal quantifier and existential quantifier.
denoted by ∀, refers to the phrase “for all” or “for every” or “for each”. It asserts that the formula for any value of 𝑦 (the value as being taken from some given universe or the set of objects of interest).
universal quantifier
denoted by ∃, refers to the phrase “there exists” or “for at least one” or “for some”. It asserts that the formula holds for at least one value of 𝑦.
existential quantifier
Give any proposition “p”, its opposite is a statement “not p” referred to as the “negation” of the given proposition “p”. Likewise, “p” is the negation of “not p”.
Definition: If p is true, then ~p is false; and if p is false, then ~p is true.
Negation
A compound statement formed by connecting two statements with the word “and” is called a ___. In symbols, it is written as “p ∧ q” which is read as “p and q”.
Definition: If p and q are true, then p ∧ q is true; otherwise p ∧ q is false.
Conjunctions
A compound statement formed by connecting two statements with the word “or” is called ???. Symbolically, “p ∨ q” which is read as “p or q”.
Definition: If p and q are false, then p ∨ q is false; otherwise p ∨ q is true.
Disjunctions
A compound statement formed by connecting two statements with the words “if…then” is called a ????. Symbolically, “p → q” which is read as “If p, then q” or “p implies q”.
The statement p is called antecedent and q is the consequent.
Conditional
A compound statement formed by connecting two statements with the word “or” is called ???. Symbolically, “p ⨁ q” which is read as “p exclusive or q”.
Definition: Proposition is true when exactly one of its proposition is true and the other one is false.
exclusive or.
A compound statement formed by connecting two statements with the words “if and only if” is called a ???. Symbolically, “p ↔ q” which read as “p if and only if q”.
Biconditional and Equivalent Statements
The three important classes of compound statements namely ?,? and ?.
tautology, contradiction and contingency.
A compound statement is a ? if its truth value is always T, regardless of the truth values of the statements of which it is composed.
Example:
The statement 𝑝→(𝑝∨𝑞) is a tautology.
tautology
A compound statement is a ? if is truth value is always F, regardless of the truth values of its variables.
Example: The statement (𝑝∧~𝑞)∧(𝑝∧𝑞) is a contradiction.
contradiction
A compound statement is a ? if it is neither tautology nor contradiction.
Example: The statement ((𝑝→𝑞)∧𝑞)→𝑝 is a contingency.
contingency
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