Truth Tables

Equivalence by Table

Two formulas are equivalent when every output row matches.

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

Example

Two formulas are equivalent when every output row matches.

highlighted = computed this step

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0expr=0 XOR=0 match=yes\begin{array}{c|c}\text{A=0 B=0}&\hlmath{\text{expr=0 XOR=0 match=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0expr=0 XOR=0 match=yesA=0 B=1expr=1 XOR=1 match=yes\begin{array}{c|c}\text{A=0 B=0}&\text{expr=0 XOR=0 match=yes}\\\text{A=0 B=1}&\hlmath{\text{expr=1 XOR=1 match=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0expr=0 XOR=0 match=yesA=0 B=1expr=1 XOR=1 match=yesA=1 B=0expr=1 XOR=1 match=yes\begin{array}{c|c}\text{A=0 B=0}&\text{expr=0 XOR=0 match=yes}\\\text{A=0 B=1}&\text{expr=1 XOR=1 match=yes}\\\text{A=1 B=0}&\hlmath{\text{expr=1 XOR=1 match=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0expr=0 XOR=0 match=yesA=0 B=1expr=1 XOR=1 match=yesA=1 B=0expr=1 XOR=1 match=yesA=1 B=1expr=0 XOR=0 match=yes\begin{array}{c|c}\text{A=0 B=0}&\text{expr=0 XOR=0 match=yes}\\\text{A=0 B=1}&\text{expr=1 XOR=1 match=yes}\\\text{A=1 B=0}&\text{expr=1 XOR=1 match=yes}\\\text{A=1 B=1}&\hlmath{\text{expr=0 XOR=0 match=yes}}\end{array}

Read the table verdict

Compute the highlighted logic-table value.

A=0 B=0expr=0 XOR=0 match=yesA=0 B=1expr=1 XOR=1 match=yesA=1 B=0expr=1 XOR=1 match=yesA=1 B=1expr=0 XOR=0 match=yesverdictequivalent: all rows match\begin{array}{c|c}\text{A=0 B=0}&\text{expr=0 XOR=0 match=yes}\\\text{A=0 B=1}&\text{expr=1 XOR=1 match=yes}\\\text{A=1 B=0}&\text{expr=1 XOR=1 match=yes}\\\text{A=1 B=1}&\text{expr=0 XOR=0 match=yes}\\\text{verdict}&\hlmath{\text{equivalent: all rows match}}\end{array}