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Logic reference

Logic definitions reference sheet

Introduce propositions, logical operators, compound expressions and truth tables with a printable reference. Use clear examples before starting symbolic logic practice.

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Read each definition and example. Use the negation table to see how a truth value changes.

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Give the symbols something to name

A proposition is a whole statement. Use familiar true and false numerical statements before replacing them with p or q.

The reference introduces the vocabulary and a small negation table. Its content is fixed; paper size, printed language and a page note can change.

Learning objective

What this activity builds

Distinguish a proposition from a question or command, and explain how logical operators build compound statements.

Worked example

Is “8 is even” a proposition? What is its negation?

Yes. Its negation is “8 is not even.”

The original statement has a definite truth value: true. Negating that same statement changes its truth value to false.

Teaching notes

Make the practice count

  • Compare a statement with a question such as “Is 8 even?”
  • Keep the proposition unchanged when adding a negation.
  • Use p and q as names for complete statements.
  • Read the table one row at a time before introducing more operators.

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2 reference pages
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Math SheetNameScoreTeacherDateLogic DefinitionsUse the definitions, examples and truth table to read compound propositions.T = True; F = FalsePropositions and expressionsA proposition has one truth value, T or F. Logical operators negate or join propositions. The result is a compoundexpression. A truth table lists its value for every assignment.pNegationNegation reverses the truth value while preserving the original proposition.(p)p(p)TFFTConjunction and disjunctionAND needs both parts true. Inclusive OR needs at least one part true.(pq)ConditionalA conditional is false only when its antecedent is true and its consequent is false.(pq)BiconditionalA biconditional is true when both parts have the same truth value.(pq)math-sheet.comPage 1 / 2
Math SheetNameScoreTeacherDateLogic DefinitionsUse the definitions, examples and truth table to read compound propositions.T = True; F = FalseExclusive ORExclusive OR means either part is true, but not both.(pq)math-sheet.comPage 2 / 2

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