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SPM Mathematics Glossary

Logical Reasoning, terms

StatementA sentence that is either true or false, but not both; a question or command is not a statement.NegationThe opposite of a statement, which reverses its truth value.ImplicationA statement of the form "if p, then q", linking a condition to a conclusion.ArgumentA set of premises leading to a conclusion; it is valid when the conclusion follows from the premises.Conjunction (“and”)A compound statement joined by “and”, true only when both parts are true.Disjunction (“or”)A compound statement joined by “or”, true when at least one part is true.ConverseThe statement formed by swapping the antecedent and consequent of an implication.Deductive reasoningReasoning from a general rule to a specific case.Inductive reasoningReasoning from specific cases to a general pattern or rule.QuantifierA word such as “all” or “some” stating how many cases a statement covers.Counter-exampleA single case that shows a general statement is false.

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Frequently asked questions

Which logical-reasoning terms should I learn first?

Begin with statement and negation, since every other term builds on being able to tell a true or false statement apart from its opposite. From there, move to implication and its converse, then conjunction and disjunction, these connect statements together and appear constantly in later questions.

What terms in logical reasoning are easiest to mix up?

Implication and converse confuse many students: swapping "if p then q" to "if q then p" changes the statement's truth value, so the two are not interchangeable. Deductive and inductive reasoning are also often swapped, deductive draws a certain conclusion from given premises, inductive generalises from a pattern.

How do logical-reasoning terms appear in exam questions?

Typical instructions include "write the negation of", "state the converse of the implication", and "determine whether the argument is valid". Questions on quantifiers ask you to judge statements using "all" or "some", while others ask you to give a counter-example to disprove a statement.

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