Inference

Implication Contrapositive

A conditional and its contrapositive match row by row.

Example

A conditional and its contrapositive match row by row.

highlighted = computed this step

Build the concrete table

Compute the highlighted logic-table value.

P=0 Q=0imp=1 contra=1 match=yes\begin{array}{c|c}\text{P=0 Q=0}&\hlmath{\text{imp=1 contra=1 match=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

P=0 Q=0imp=1 contra=1 match=yesP=0 Q=1imp=1 contra=1 match=yes\begin{array}{c|c}\text{P=0 Q=0}&\text{imp=1 contra=1 match=yes}\\\text{P=0 Q=1}&\hlmath{\text{imp=1 contra=1 match=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

P=0 Q=0imp=1 contra=1 match=yesP=0 Q=1imp=1 contra=1 match=yesP=1 Q=0imp=0 contra=0 match=yes\begin{array}{c|c}\text{P=0 Q=0}&\text{imp=1 contra=1 match=yes}\\\text{P=0 Q=1}&\text{imp=1 contra=1 match=yes}\\\text{P=1 Q=0}&\hlmath{\text{imp=0 contra=0 match=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

P=0 Q=0imp=1 contra=1 match=yesP=0 Q=1imp=1 contra=1 match=yesP=1 Q=0imp=0 contra=0 match=yesP=1 Q=1imp=1 contra=1 match=yes\begin{array}{c|c}\text{P=0 Q=0}&\text{imp=1 contra=1 match=yes}\\\text{P=0 Q=1}&\text{imp=1 contra=1 match=yes}\\\text{P=1 Q=0}&\text{imp=0 contra=0 match=yes}\\\text{P=1 Q=1}&\hlmath{\text{imp=1 contra=1 match=yes}}\end{array}

Read the table verdict

Compute the highlighted logic-table value.

P=0 Q=0imp=1 contra=1 match=yesP=0 Q=1imp=1 contra=1 match=yesP=1 Q=0imp=0 contra=0 match=yesP=1 Q=1imp=1 contra=1 match=yesverdictequivalent\begin{array}{c|c}\text{P=0 Q=0}&\text{imp=1 contra=1 match=yes}\\\text{P=0 Q=1}&\text{imp=1 contra=1 match=yes}\\\text{P=1 Q=0}&\text{imp=0 contra=0 match=yes}\\\text{P=1 Q=1}&\text{imp=1 contra=1 match=yes}\\\text{verdict}&\hlmath{\text{equivalent}}\end{array}
logic-computation Every row is intentionally ordered and pinned to the lesson specification.