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In propositional logic, disjunction elimination [1] [2] (sometimes named proof by cases, case analysis, or or elimination) is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof.
Examples: The column-14 operator (OR), shows Addition rule : when p =T (the hypothesis selects the first two lines of the table), we see (at column-14) that p ∨ q =T. We can see also that, with the same premise, another conclusions are valid: columns 12, 14 and 15 are T.
For example, the rule of inference called modus ponens takes two premises, one in the form "If p then q" and another in the form "p", and returns the conclusion "q". The rule is valid with respect to the semantics of classical logic (as well as the semantics of many other non-classical logics ), in the sense that if the premises are true (under ...
There are ten primitive rules of proof, which are the rule assumption, plus four pairs of introduction and elimination rules for the binary connectives, and the rule reductio ad adbsurdum. [17] Disjunctive Syllogism can be used as an easier alternative to the proper ∨-elimination, [ 17 ] and MTT and DN are commonly given rules, [ 22 ...
The rule makes it possible to shorten longer proofs by deriving one of the conjuncts of a conjunction on a line by itself. An example in English: It's raining and it's pouring. Therefore it's raining. The rule consists of two separate sub-rules, which can be expressed in formal language as: and
Static-0 Hazard: the output is currently 0 and after the inputs change, the output momentarily changes to 1,0 before settling on 0; In properly formed two-level AND-OR logic based on a Sum Of Products expression, there will be no static-0 hazards (but may still have static-1 hazards).
The rule has the restrictions that the constant c introduced by the rule must be a new term that has not occurred earlier in the proof, and it also must not occur in the conclusion of the proof. It is also necessary that every instance of x {\displaystyle x} which is bound to ∃ x {\displaystyle \exists x} must be uniformly replaced by c .
The Western Electric rules are decision rules in statistical process control for detecting out-of-control or non-random conditions on control charts. [1] Locations of the observations relative to the control chart control limits (typically at ±3 standard deviations) and centerline indicate whether the process in question should be investigated for assignable causes.