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

$|AB|^2=|BC|^2+|AC|^2$ .

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 $|AB|^2=|BC|^2+|AC|^2$

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 $|AB|^2=|BC|^2+|AC|^2$
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 $|AB|^2=|BC|^2+|AC|^2$

True

Contrapositive statement:

if The sides of triangle ABC are not such that $|AB|^2=|BC|^2+|AC|^2$ then Triangle ABC is not a right triangle with m(C)=90°

True

4 0

4 years ago

Help on # three it’s due in 10 minuets!!

LuckyWell [14K]

16 = 48/3
48 divided by 2 = 24
There is 24 students in the club.

6 0

4 years ago

What is the linear equation: y=-5x-3 in standard form

tester [92]

5x+y=-3 is the standard form

8 0

3 years ago