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Logic reference

Truth tables reference sheet

Print truth tables for NOT, AND, OR, conditional, biconditional and exclusive OR. Compare their truth conditions in individual tables and a combined reference.

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Reference · LetterReference · A4
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Read T as true and F as false. Compare the output column for the same input row across operators.

Download the complete reference, including every page of explanations and tables. This fixed handout has no separate answer key.

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Reference handout
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Compare the same row across operators

AND, inclusive OR, conditional, biconditional and exclusive OR answer different questions about the same two input values.

T and F remain the printed notation in every supported language. A translated legend explains what they mean. Download the complete reference to see every table.

Learning objective

What this activity builds

Use a truth table to distinguish the meanings of logical connectives across every input case.

Worked example

When p is true and q is false, what is p → q?

False.

The conditional fails when its hypothesis is true but its conclusion is false. Its other three input cases are true.

Teaching notes

Make the practice count

  • Keep the input order TT, TF, FT, FF consistent.
  • Compare OR and exclusive OR on the TT row.
  • Read a biconditional as a match between truth values.
  • Use the reference beside a focused practice sheet, then cover it for a recall check.

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3 reference pages
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Math SheetNameScoreTeacherDateTruth Tables ReferenceCompare the truth conditions for the standard logical connectives.T = True; F = FalseNOTNOT is true exactly when its input is false.(p)p(p)TFFTANDAND is true only when both inputs are true.(pq)pq(pq)TTTTFFFTFFFFOROR is true when at least one input is true.(pq)pq(pq)TTTTFTFTTFFFmath-sheet.comPage 1 / 3
Math SheetNameScoreTeacherDateTruth Tables ReferenceCompare the truth conditions for the standard logical connectives.T = True; F = FalseIMPLIESA conditional is false only for a true antecedent and false consequent.(pq)pq(pq)TTTTFFFTTFFTIFFA biconditional is true when both inputs agree.(pq)pq(pq)TTTTFFFTFFFTXORXOR is true when exactly one input is true.(pq)pq(pq)TTFTFTFTTFFFmath-sheet.comPage 2 / 3
Math SheetNameScoreTeacherDateTruth Tables ReferenceCompare the truth conditions for the standard logical connectives.T = True; F = FalseTruth tableT = True; F = Falsepq(p)(pq)(pq)(pq)(pq)(pq)TTFTTTTFTFFFTFFTFTTFTTFTFFTFFTTFmath-sheet.comPage 3 / 3

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