Inference

Modus Ponens Validity

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

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.

P=0 Q=0P_and_imp=0 Q=0 valid_row=yes\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.

P=0 Q=0P_and_imp=0 Q=0 valid_row=yesP=0 Q=1P_and_imp=0 Q=1 valid_row=yes\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.

P=0 Q=0P_and_imp=0 Q=0 valid_row=yesP=0 Q=1P_and_imp=0 Q=1 valid_row=yesP=1 Q=0P_and_imp=0 Q=0 valid_row=yes\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.

P=0 Q=0P_and_imp=0 Q=0 valid_row=yesP=0 Q=1P_and_imp=0 Q=1 valid_row=yesP=1 Q=0P_and_imp=0 Q=0 valid_row=yesP=1 Q=1P_and_imp=1 Q=1 valid_row=yes\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.

P=0 Q=0P_and_imp=0 Q=0 valid_row=yesP=0 Q=1P_and_imp=0 Q=1 valid_row=yesP=1 Q=0P_and_imp=0 Q=0 valid_row=yesP=1 Q=1P_and_imp=1 Q=1 valid_row=yesverdictvalid: no counterexample\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}
logic-computation Every row is intentionally ordered and pinned to the lesson specification.