Question

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

Answer 1

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.