The number k is a positive integer if and only if 5k is a natural number. The given statement is False; 5k = 1, then k = 1/5, which is not a positive integer.
An example of a biconditional statement is
the shape:
If and only if Q, then P.
P and Q are two given propositions.
We'll see that choice D is the right one."
false; if k = 1/5 and 5k = 1, then k is not a
a positive number"
P if and only if the biconditional statement is true.
Q.
suggests that
P must be true for Q to be true.
Q must be true for P to be true.
If Q is untrue, P must also be false.
P must be untrue for Q to be false.
This is the statement:
Remember that "5'k is a natural number" now is possible if
k = (1/5)
The answer is 5"(1/5) = 1, which is a natural number.
In some circumstances, 5k can be a natural number.
When k (for example) is not a positive number
for illustration, or k = 1/5, 2/5, etc.
We have just discovered a counterexample.
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