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
