A statement in the form p→q has three related implications that are called converse, inverse, and contrapositive.
A statement in the form p→q has three related implications.
Statement: If p then q (p→q)
Converse: If q then p (q→p)
Inverse: If not p then not q (-p → -q)
Contrapositive: If not q then not p (-q → -p)
For the given implications, its converse, inverse, and contrapositive can be written as.
Given statement:
(a) If a quadrilateral is a parallelogram, then its opposite sides are congruent then its converse, inverse, and contrapositive are:
Converse: If a quadrilateral has opposite sides that are congruent then it's a parallelogram.
Inverse: If a quadrilateral is not a parallelogram then its opposite sides are not congruent.
Contrapositive: If a quadrilateral has opposite sides that are not congruent then it's not a parallelogram.
(b) If two lines do not intersect, then they are parallel:
Converse: If the two lines do not intersect in the same plane, then they are parallel.
Contrapositive: If the two lines intersect in the same plane, then they are not parallel.
(c) If the sky does not look blue, then it is not nighttime:
Converse: If it is not nighttime, then the sky looks blue.
Inverse: If the sky does not look blue then it is nighttime.
Contrapositive: If it is nighttime then the sky does not look blue.
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