aConverse: If the cat runs away frightened, then the cat knocked over the lamp.
Converse true? No
B
bConverse: If the chances of getting a 3 are 16, then a 6-sided die is rolled.
Converse true? No
C
cConverse: If a triangle is a right triangle, then it has a 90^(∘) angle.
Converse true? Yes
Practice makes perfect
a Let's highlight the hypothesis and conclusion in the conditional statement.
If the cat knocked over the lamp,
then it will run away frightened.
The converse of a conditional statement, q→ p, exchanges the hypothesis and the conclusion of the conditional statement.
If the cat runs away frightened,
then the cat knocked over the lamp.
Even if the original statement is true, the converse is not necessarily true as their could be other reasons why the cat ran away frightened.
b Like in Part A, we will highlight the hypothesis and conclusion in the conditional statement.
If a 6-sided die is rolled,
then the chances of getting a 3 are $ 16$.
Again, to get the converse of the conditional statement, q→ p, we exchange the hypothesis and the conclusion of the conditional statement.
If the chances of getting a 3 are $ 16$,
then a 6-sided die is rolled.
Even if the original statement is true, the converse is not necessarily true as their could be other types of dice where the chances of rolling a 3 is 16.
c Like in Parts A and B, we will highlight the hypothesis and conclusion in the conditional statement.
If a triangle has a $90^(∘)$ angle,
then it is a right triangle.
Again, to get the converse of the conditional statement, q→ p, we exchange the hypothesis and the conclusion of the conditional statement.
If a triangle is a right triangle,
then it has a $90^(∘)$ angle.
This statement is true as all right triangles have a 90^(∘) angle.
