Strength of Negation Question - Necessary Assumption

[BorisJ159]

I had a question as to the proper way of negating answer choices for necessary assumption questions. When you get something like the following example:

Exercise promotes good health.

Is the logical negation

1. Exercise does not necessarily promote good health. OR

2. Exercise does not promote good health.


I'm leaning toward the 1st being right since 2 seems too strong, but what I've studied indicates that 2 is the right way. Or, does it not matter? I'm quite confused about this.

[ohthatpatrick]

It'll always be accurate to say negate a claim by saying ...

it is not true that ....[claim]

From there, we try to interpret what that would mean. If we say "it is not true that exercise promotes good health", are we saying,
1. exercise does not promote good health
or
2. exercise does not always promote good health
?

Honestly, I don't think there's a real answer or that it will matter a ton. I tend to think of it as #1, whereas our books would say #2.

Thinking of it as #1 has never steered me in the wrong direction.

If you were negating something presented as a conditional, then I would use the "not necessarily" form.
Otherwise, I would just switch the main verb from "promotes" to "does not promote".

i.e., if an answer choice were presented as
(A) If you exercise, you'll have good health

then my negation would be "It's possible to exercise but not have good health" (that's essentially the not-necessarily formulation)

if it said
(A) exercising promotes good health

then my negation would be "exercising does not promote good health".


Hope this helps.