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Truth table shortcuts

Classifying sentences without filling in every row, stopping as soon as the entries found settle whether a tautology or contradiction is possible.

forall x: Calgary, Truth table shortcuts

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1 exercise

Exercise A

Using shortcuts, determine whether each sentence is a tautology, a contradiction, or neither.

$\neg B\wedge B$
$\neg D\vee D$
$(A\wedge B)\vee(B\wedge A)$
$\neg[A\rightarrow(B\rightarrow A)]$
$A\leftrightarrow[A\rightarrow(B\wedge\neg B)]$
$\neg(A\wedge B)\leftrightarrow A$
$A\rightarrow(B\vee C)$
$(A\wedge\neg A)\rightarrow(B\vee C)$
$(B\wedge D)\leftrightarrow[A\leftrightarrow(A\vee C)]$

Adapted from forall x: Calgary © 2025 P. D. Magnus, Tim Button, Robert Trueman, and Richard Zach. Licensed under CC BY 4.0. Source: forall x: Calgary. Imported at revision ec34df8.