kaitlynnhattabaugh
Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Determine whether the biconditional statement is true or false. If false, give a counterexample.

The number k is a positive integer if and only if 5k is a natural number.


A. true
B. false; 5k = 1, then k = −1/5, which is not a positive integer
C. false; 5k = 25, then k = 5 which is not a positive integer
D. false; 5k = 1, then k = 1/5, which is not a positive integer

Sagot :

facundo3141592

A biconditional statement is something of the form:

P if and only if Q.

For two given propositions P and Q.

We will see that the correct option is D: " false; 5k = 1, then k = 1/5, which is not a positive integer"

The biconditional statement: P if and only if Q.

implies that:

If P is true, then Q is true.

If Q is true, then P is true.

if Q is false, then P is false

if P is false, then Q is false.

Here the statement is:

"The number k is a positive integer if and only if 5k is a natural number"

Now, notice that "5*k is a natural number" can be true if:

k = (1/5)

So we get: 5*(1/5) = 1 is a natural number.

So 5k can be a natural number in cases where k is not a positive integer (for example, or k = 1/5, 2/5, etc...)

So we just found a counterexample of the statement, thus the statement is false, and the correct option is D "false; 5k = 1, then k = 1/5, which is not a positive integer"

If you want to learn more, you can read:

https://brainly.com/question/17681179

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.