Modus Ponens Validity - Logic, Gates, and Computation Step by Step

An argument is valid when no row makes premises true and conclusion false.

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

Example

An argument is valid when no row makes premises true and conclusion false.

highlighted = computed this step

Build the concrete table

Compute the highlighted logic-table value.

\begin{array}{c|c}\text{P=0 Q=0}&\hlmath{\text{P\_and\_imp=0 Q=0 valid\_row=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

\begin{array}{c|c}\text{P=0 Q=0}&\text{P\_and\_imp=0 Q=0 valid\_row=yes}\\\text{P=0 Q=1}&\hlmath{\text{P\_and\_imp=0 Q=1 valid\_row=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

\begin{array}{c|c}\text{P=0 Q=0}&\text{P\_and\_imp=0 Q=0 valid\_row=yes}\\\text{P=0 Q=1}&\text{P\_and\_imp=0 Q=1 valid\_row=yes}\\\text{P=1 Q=0}&\hlmath{\text{P\_and\_imp=0 Q=0 valid\_row=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

\begin{array}{c|c}\text{P=0 Q=0}&\text{P\_and\_imp=0 Q=0 valid\_row=yes}\\\text{P=0 Q=1}&\text{P\_and\_imp=0 Q=1 valid\_row=yes}\\\text{P=1 Q=0}&\text{P\_and\_imp=0 Q=0 valid\_row=yes}\\\text{P=1 Q=1}&\hlmath{\text{P\_and\_imp=1 Q=1 valid\_row=yes}}\end{array}

Read the table verdict

Compute the highlighted logic-table value.

\begin{array}{c|c}\text{P=0 Q=0}&\text{P\_and\_imp=0 Q=0 valid\_row=yes}\\\text{P=0 Q=1}&\text{P\_and\_imp=0 Q=1 valid\_row=yes}\\\text{P=1 Q=0}&\text{P\_and\_imp=0 Q=0 valid\_row=yes}\\\text{P=1 Q=1}&\text{P\_and\_imp=1 Q=1 valid\_row=yes}\\\text{verdict}&\hlmath{\text{valid: no counterexample}}\end{array}