99.4k views
2 votes
Suppose that p(n) is a propositional function. for which positive integers n, p(n) is true if we prove that:_______

is true
p(2)
p(3)
p(4)
p(6)
all of the above none of the above

1 Answer

4 votes

Final answer:

To determine for which positive integers n the propositional function p(n) is true, we need to examine each individual proposition for truth. The correct answer is All of the above.

Step-by-step explanation:

To determine for which positive integers n the propositional function p(n) is true, we need to examine each individual proposition for truth. Let's go through each option:

p(2): This means we substitute n with 2 in p(n), so we have p(2). If p(2) is true, then 2 is a positive integer for which p(n) is true.

p(3): Similarly, substituting n with 3 gives us p(3). If p(3) is true, then 3 is a positive integer for which p(n) is true.

p(4): Substituting 4 for n, we have p(4). If p(4) is true, then 4 is a positive integer for which p(n) is true.

p(6): Substituting 6 for n, we have p(6). If p(6) is true, then 6 is a positive integer for which p(n) is true.

All of the above: This means that all of p(2), p(3), p(4), and p(6) are true, so 2, 3, 4, and 6 are all positive integers for which p(n) is true.

Therefore, the correct answer is All of the above.

User WouterH
by
8.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.