Deductive Reasoning
Draw necessary conclusions from given facts
Deductive reasoning tests whether a conclusion must be true when the given statements are true. It moves from a rule to a case or combines premises into a necessary result. In aptitude questions, use only the information provided, preserve words such as all, no and some, and reject a conclusion that is merely possible.
Key formulas and rules
4 rulesis modus ponens: a valid inference.
is modus tollens: a valid inference.
affirms the consequent and is invalid.
denies the antecedent and is invalid.
Key concepts
Premises, conclusions and validity
An argument has one or more premises and a conclusion. A deductive argument is valid when the premises make it impossible for the conclusion to be false. Validity describes the structure, not whether the premises are actually true. A sound argument is valid and also has true premises.
Conditional statements
In an if-then statement, the if-part is the antecedent and the then-part is the consequent. From If P, then Q and P, you may conclude Q. From If P, then Q and not Q, you may conclude not P. Do not reverse the rule: Q does not by itself prove P.
Necessary and sufficient conditions
If P is sufficient for Q, then P guarantees Q, written P implies Q. Q is necessary for P because P cannot occur without Q. A necessary condition does not automatically cause the result. For example, a valid password may be necessary for login, but it may not be sufficient if a second factor is also required.