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The conjunction fallacy (also known as the Linda problem) is an inference that a conjoint set of two or more specific conclusions is likelier than any single member of that same set, in violation of the laws of probability.
In ordinary language terms, if both p and q are true, then the conjunction p ∧ q is true. For all other assignments of logical values to p and to q the conjunction p ∧ q is false. It can also be said that if p, then p ∧ q is q, otherwise p ∧ q is p.
In classical logic, logical conjunction is an operation on two logical values, ... as well as prove the conjunction false: ) In other words, a conjunction can ...
False authority (single authority) – using an expert of dubious credentials or using only one opinion to promote a product or idea. Related to the appeal to authority. False dilemma (false dichotomy, fallacy of bifurcation, black-or-white fallacy) – two alternative statements are given as the only possible options when, in reality, there ...
Conjunction introduction / elimination; ... where T = true and F = false, and, the columns are the logical operators: 0, false, Contradiction;
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 ...
These examples, one from mathematics and one from natural language, illustrate the concept of vacuous truths: "For any integer x, if x > 5 then x > 3." [11] – This statement is true non-vacuously (since some integers are indeed greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement implies the vacuous truth that "if 2 > 5 ...
For instance, two statements or more are logically incompatible if, and only if their conjunction is logically false. One statement logically implies another when it is logically incompatible with the negation of the other. A statement is logically true if, and only if its opposite is logically false. The opposite statements must contradict one ...