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In Disjunctive Syllogism, the first premise establishes two options. The second takes one away, so the conclusion states that the remaining one must be true. [3] It is shown below in logical form. Either A or B Not A Therefore B. When A and B are replaced with real life examples it looks like below.
The reasoning is simple: since at least one of the statements P and R is true, and since either of them would be sufficient to entail Q, Q is certainly true. An example in English: If I'm inside, I have my wallet on me. If I'm outside, I have my wallet on me. It is true that either I'm inside or I'm outside. Therefore, I have my wallet on me.
The second premise is an assertion that P, the antecedent of the conditional claim, is the case. From these two premises it can be logically concluded that Q, the consequent of the conditional claim, must be the case as well. An example of an argument that fits the form modus ponens: If today is Tuesday, then John will go to work. Today is Tuesday.
A syllogism takes the form (note: M – Middle, S – subject, P – predicate.): Major premise: All M are P. Minor premise: All S are M. Conclusion/Consequent: All S are P. The premises and conclusion of a syllogism can be any of four types, which are labeled by letters [14] as follows. The meaning of the letters is given by the table:
Classical logic is the standard logic of mathematics. Many mathematical theorems rely on classical rules of inference such as disjunctive syllogism and the double negation elimination. The adjective "classical" in logic is not related to the use of the adjective "classical" in physics, which has another meaning.
Because the logical or means a disjunction formula is true when either one or both of its parts are true, it is referred to as an inclusive disjunction. This is in contrast with an exclusive disjunction, which is true when one or the other of the arguments are true, but not both (referred to as exclusive or, or XOR).
An argument map or argument diagram is a visual representation of the structure of an argument. An argument map typically includes all the key components of the argument, traditionally called the conclusion and the premises , also called contention and reasons . [ 1 ]
Since logical connectives are defined semantically only in terms of the truth values that they take when the propositional variables that they're applied to take either of the two possible truth values, [1] [34] the semantic definition of the connectives is usually represented as a truth table for each of the connectives, [1] [34] [70] as seen ...