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The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), [2] and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of ...
Venn diagram of (true part in red) In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or bidirectional implication or biimplication or bientailment, is the logical connective used to conjoin two statements and to form the statement "if and only if" (often abbreviated as "iff " [1]), where is known as the antecedent, and the consequent.
The column-11 operator (IF/THEN), shows Modus ponens rule: when p→q=T and p=T only one line of the truth table (the first) satisfies these two conditions. On this line, q is also true. Therefore, whenever p → q is true and p is true, q must also be true.
To read the truth-value assignments for the operation from top to bottom on its truth table is the same as taking the complement of reading the table of the same or another connective from bottom to top. Without resorting to truth tables it may be formulated as g̃(¬a 1, ..., ¬a n) = ¬g(a 1, ..., a n). E.g., ¬. Truth-preserving
An example: we are given the conditional fact that if it is a bear, then it can swim. Then, all 4 possibilities in the truth table are compared to that fact. If it is a bear, then it can swim — T; If it is a bear, then it can not swim — F; If it is not a bear, then it can swim — T because it doesn’t contradict our initial fact.
In logic, a truth function [1] is a function that accepts truth values as input and produces a unique truth value as output. In other words: the input and output of a truth function are all truth values; a truth function will always output exactly one truth value, and inputting the same truth value(s) will always output the same truth value.
A three-valued logic where the third truth value is the truth-value gap "neither true nor false" ("N"), and the designated values are "true" and "neither true nor false." [10] analysis 1. Analysis, the process of breaking a concept down into more simple parts, so that its logical structure is displayed. 2. Mathematical analysis analytic
Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions . In other words, a logical truth is a statement which is not only true, but one which is true under all interpretations of its logical components ...