Inference

Tautology vs Contradiction

One expression is always true; the other is never true.

logic-computation Every row is intentionally ordered and pinned to the lesson specification.

Example

One expression is always true; the other is never true.

highlighted = computed this step

Build the concrete table

Compute the highlighted logic-table value.

A=0A OR notA=1 A AND notA=0\begin{array}{c|c}\text{A=0}&\hlmath{\text{A OR notA=1 A AND notA=0}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0A OR notA=1 A AND notA=0A=1A OR notA=1 A AND notA=0\begin{array}{c|c}\text{A=0}&\text{A OR notA=1 A AND notA=0}\\\text{A=1}&\hlmath{\text{A OR notA=1 A AND notA=0}}\end{array}

Read the table verdict

Compute the highlighted logic-table value.

A=0A OR notA=1 A AND notA=0A=1A OR notA=1 A AND notA=0verdicttautology=always 1, contradiction=always 0\begin{array}{c|c}\text{A=0}&\text{A OR notA=1 A AND notA=0}\\\text{A=1}&\text{A OR notA=1 A AND notA=0}\\\text{verdict}&\hlmath{\text{tautology=always 1, contradiction=always 0}}\end{array}