Laws and Normal Forms

De Morgan by Table

A law is a row-by-row equality, not a magic rewrite.

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

Example

A law is a row-by-row equality, not a magic rewrite.

highlighted = computed this step

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0left=1 right=1 match=yes\begin{array}{c|c}\text{A=0 B=0}&\hlmath{\text{left=1 right=1 match=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

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

Build the concrete table

Compute the highlighted logic-table value.

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

Build the concrete table

Compute the highlighted logic-table value.

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

Read the table verdict

Compute the highlighted logic-table value.

A=0 B=0left=1 right=1 match=yesA=0 B=1left=1 right=1 match=yesA=1 B=0left=1 right=1 match=yesA=1 B=1left=0 right=0 match=yesverdictDe Morgan law holds\begin{array}{c|c}\text{A=0 B=0}&\text{left=1 right=1 match=yes}\\\text{A=0 B=1}&\text{left=1 right=1 match=yes}\\\text{A=1 B=0}&\text{left=1 right=1 match=yes}\\\text{A=1 B=1}&\text{left=0 right=0 match=yes}\\\text{verdict}&\hlmath{\text{De Morgan law holds}}\end{array}