Write the contrapositive and converse of the following statement:
If two lines are parallel,then they do not intersect in the same plane.
If two lines are parallel,then they do not intersect in the same plane.
(N/A) Let $p$ be the statement: "Two lines are parallel".
Let $q$ be the statement: "They do not intersect in the same plane".
The given statement is of the form "If $p$,then $q$ $(p \implies q)$".
The contrapositive is "If not $q$,then not $p$ $(\neg q \implies \neg p)$":
If two lines intersect in the same plane,then they are not parallel.
The converse is "If $q$,then $p$ $(q \implies p)$":
If two lines do not intersect in the same plane,then they are parallel.
Let $q$ be the statement: "They do not intersect in the same plane".
The given statement is of the form "If $p$,then $q$ $(p \implies q)$".
The contrapositive is "If not $q$,then not $p$ $(\neg q \implies \neg p)$":
If two lines intersect in the same plane,then they are not parallel.
The converse is "If $q$,then $p$ $(q \implies p)$":
If two lines do not intersect in the same plane,then they are parallel.
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