Deductive Reasoning
Deductive Reasoning asks what must be true given the stated rules. If the premises are true and the logic is valid, the conclusion follows with certainty. The test is whether you can separate must from could.
Concepts to master
- Conditional statements: "If P, then Q." P is sufficient for Q; Q is necessary for P.
- Valid inferences: from "If P then Q" and "P," you may conclude Q. From "If P then Q" and "not Q," you may conclude "not P."
- Invalid inferences: from "If P then Q" and "Q," you may not conclude P. From "not P," you may not conclude "not Q."
- Quantifiers: all, some, none. "All A are B" does not mean "all B are A."
- Either/or and unless: "unless" means "if not."
Traps that appear
- Affirming the consequent - assuming Q proves P.
- Denying the antecedent - assuming not-P proves not-Q.
- Reversing "all" statements.
- Adding real-world assumptions the premises do not grant.
Worked example
Rule: "All officers assigned to the detail must carry a radio. Officer Ruiz is assigned to the detail."
Must be true: Ruiz carries a radio. Not necessarily true: everyone carrying a radio is on the detail. That reverses the rule.
Rule of thumb
Write the rule as an arrow: P → Q. You may travel forward from P, or backward from not-Q. Any other direction is a guess, not a deduction.