Question

Use the conditional statement to answer the question.

If a number is a prime number, then the number is odd.



Can the statement be written as a biconditional statement and why?

No, because the statement is true, but its converse is false

No, because the statement and its converse are both false

No, because the statement is false, but its converse is true

Yes, because the statement and its converse are both true

Answer 1

@563blackghost

Answer 2

odd numbers cant be prime right?

Answer 3

Actually prime numbers can be odd....

Prime: 2, 3, 5, 7, 11, 13, 17, 19 etc.

Those are all prime...

Bicoditional Statment format:

\(\LARGE{p \leftarrow \rightarrow q}\)

`p if and only if q`

Answer 4

so the statement is true right?

Answer 5

yes :)

Answer 6

First lets find the converse...

Converse Statment:
`if q, then p`

So the hypothesis is `a number is a prime number` and the conclusion is `the number is odd` so place them in each others places...

Answer 7

YaY i hit 90 SS :)

Answer 8

but the bioconditional is false right?

Answer 9

To find out if the bioconditional is false we have to see if the converse is false...if the conditional and converse is true then the bioconditional is true...

Answer 10

if a number is odd, than it is a prime number... did i put it right?

Answer 11

That is correct :)

Now lets list odd numbers...

Odd: 1, 3, 5, 7, 9, 11 etc...

Now is ever odd number listed a prime?

Answer 12

yes

Answer 13

wait not 9

Answer 14

cause its divisible by 3

Answer 15

Correct :) So the converse is not true....

So that would mean that it can not be bioconditonal cause the conditional statment is true but the converse is not ^^

Answer 16

so statement is true and converse is false

Answer 17

Correct :)

Answer 18

ok i have one thing i would like you to check