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A conditional sentence is a sentence in a natural language that expresses that one thing is contingent on another, e.g., "If it rains, the picnic will be cancelled." They are so called because the impact of the sentence’s main clause is conditional on a subordinate clause.
If P, then Q. Not Q. Therefore, not P. The first premise is a conditional ("if-then") claim, such as P implies Q. The second premise is an assertion that Q, the consequent of the conditional claim, is not the case. From these two premises it can be logically concluded that P, the antecedent of the conditional claim, is also not the case. For ...
A rule of inference is a scheme of drawing conclusions that depends only on the logical form of the premises and the conclusion but not on their specific content. [39] [40] The most-discussed rule of inference is the modus ponens. It has the following form: p; if p then q; therefore q. This scheme is deductively valid no matter what p and q ...
When the movement rule applies, it moves the auxiliary to the beginning of the sentence. [ 5 ] An alternative analysis does not acknowledge the binary division of the clause into subject NP and predicate VP, but rather it places the finite verb as the root of the entire sentence and views the subject as switching to the other side of the finite ...
An example traditionally used by logicians contrasting sufficient and necessary conditions is the statement "If there is fire, then oxygen is present". An oxygenated environment is necessary for fire or combustion, but simply because there is an oxygenated environment does not necessarily mean that fire or combustion is occurring.
For example, If P, then Q. P. ∴ Q. In this example, the first premise is a conditional statement in which "P" is the antecedent and "Q" is the consequent. The second premise "affirms" the antecedent. The conclusion, that the consequent must be true, is deductively valid.
The rule was "If the card shows an even number on one face, then its opposite face is blue." Only a card with both an even number on one face and something other than blue on the other face can invalidate this rule: If the 3 card is blue (or red), that doesn't violate the rule. The rule makes no claims about odd numbers. (Denying the antecedent)
The game host then opens one of the other doors, say 3, to reveal a goat and offers to let the player switch from door 1 to door 2. The Monty Hall problem is a brain teaser , in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal and named after its original host, Monty Hall .