Respuesta :
A conditional statement involves 2 propositions, p and q. The conditional statement, is a proposition which we write as: p⇒q,
and read "if p then q"
Let p be the proposition: Triangle ABC is a right triangle with m(C)=90°.
Let q be the proposition: The sides of triangle ABC are such that
[tex]|AB|^2=|BC|^2+|AC|^2[/tex].
An example of a conditional statement is : p⇒q, that is:
if Triangle ABC is a right triangle with m(C)=90° then The sides of triangle ABC are such that [tex]|AB|^2=|BC|^2+|AC|^2[/tex]
This compound proposition (compound because we formed it using 2 other propositions) is true. So the truth value is True,
the converse, inverse and contrapositive of p⇒q are defined as follows:
converse: q⇒p
inverse: ¬p⇒¬q (if [not p] then [not q])
contrapositive: ¬q⇒¬p
Converse of our statement:
if The sides of triangle ABC are such that [tex]|AB|^2=|BC|^2+|AC|^2[/tex]
then Triangle ABC is a right triangle with m(C)=90°
True
Inverse of the statement:
if Triangle ABC is not a right triangle with m(C) not =90° then The sides of triangle ABC are not such that [tex]|AB|^2=|BC|^2+|AC|^2[/tex]
True
Contrapositive statement:
if The sides of triangle ABC are not such that [tex]|AB|^2=|BC|^2+|AC|^2[/tex] then Triangle ABC is not a right triangle with m(C)=90°
True
and read "if p then q"
Let p be the proposition: Triangle ABC is a right triangle with m(C)=90°.
Let q be the proposition: The sides of triangle ABC are such that
[tex]|AB|^2=|BC|^2+|AC|^2[/tex].
An example of a conditional statement is : p⇒q, that is:
if Triangle ABC is a right triangle with m(C)=90° then The sides of triangle ABC are such that [tex]|AB|^2=|BC|^2+|AC|^2[/tex]
This compound proposition (compound because we formed it using 2 other propositions) is true. So the truth value is True,
the converse, inverse and contrapositive of p⇒q are defined as follows:
converse: q⇒p
inverse: ¬p⇒¬q (if [not p] then [not q])
contrapositive: ¬q⇒¬p
Converse of our statement:
if The sides of triangle ABC are such that [tex]|AB|^2=|BC|^2+|AC|^2[/tex]
then Triangle ABC is a right triangle with m(C)=90°
True
Inverse of the statement:
if Triangle ABC is not a right triangle with m(C) not =90° then The sides of triangle ABC are not such that [tex]|AB|^2=|BC|^2+|AC|^2[/tex]
True
Contrapositive statement:
if The sides of triangle ABC are not such that [tex]|AB|^2=|BC|^2+|AC|^2[/tex] then Triangle ABC is not a right triangle with m(C)=90°
True
Answer:
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