types of statements | converse, inverse, contrapositive
TRANSCRIPT
Converse, Inverse, and Contrapositive
Type of
Statement
Words Symbols
Conditional if-then form p q
Converse EXCHANGE the hypothesis and
conclusion
q p
Inverse NEGATING the hypothesis and
conclusion
p q
Contrapositive NEGATING the converse of the
conditional
q p
Ma. Irene G. Gonzales © 2015
Type of
Statement
Statements Symbolism
Conditional If animals have stripes, then they
are zebras.
p q
Converse If animals are zebras, then they
have stripes.
q p
Inverse If animals don’t have stripes, then
they are not zebras.
p q
Contrapositive If animals are not zebras, then they
don’t have stripes.
q p
Example 1: Animals with stripes are zebras.
Ma. Irene G. Gonzales © 2015
Type of
Statement
Statements Symbolism
Conditional If triangles are equilateral, then they
are equiangular.
p q
Converse If triangles are equiangular, then
they are equilateral.
q p
Inverse If triangles are not equilateral, then
they are not equiangular.
p q
Contrapositive If triangles are not equiangular,
then they are not equilateral.
q p
Example 2: Equilateral triangles are equiangular.
Ma. Irene G. Gonzales © 2015
Type of
Statement
Statements Symbolism
Conditional If it is a whole number, then it is an
integer.
p q
Converse If it is an integer, then it is a whole
number.
q p
Inverse If it is not a whole number, then it is
not an integer.
p q
Contrapositive If it is not an integer, then it is not a
whole number.
q p
Example 3: All whole numbers are integers.
Ma. Irene G. Gonzales © 2015
Type of
Statement
Statements Symbolism
Conditional If two lines intersect, then they lie
in only one plane.
p q
Converse If two lines lie in one plane, then
they intersect.
q p
Inverse If two lines do not intersect, then
they do not lie in only one plane.
p q
Contrapositive If two lines do not lie in one plane,
then they do not intersect.
q p
Example 4: Two intersecting lines lie in only one plane.
Ma. Irene G. Gonzales © 2015
Type of
Statement
Statements Symbolism
Conditional If it is a whole number, then it is an
integer.
p q
Converse If it is an integer, then it is a whole
number.
q p
Inverse If it is not a whole number, then it is
not an integer.
p q
Contrapositive If it is not an integer, then it is not a
whole number.
q p
Example 5: An equilateral triangle is isosceles.
Ma. Irene G. Gonzales © 2015