The word whether indicates that there is a choice
or a doubt between two alternatives. After the word whether,
the words or not are necessary in some cases, but optional
in other cases, as in your two sentences.
The New York Times Manual of Style and Usage (Random House,
1999, p.355) says that when a whether clause
modifies a verb, or not is needed:
Theyll play tomorrow whether or not it rains.
(The clause [with whether] modifies play.)
Other examples of sentences like this would be:
The project will continue whether or not the researchers
receive a government grant.
The project will continue whether the researchers
receive a government grant or not.
(The clause beginning with whether modifies continue.)
Ill call you tomorrow whether or not I have
the answer for you then.
Ill call you tomorrow whether I have the answer
for you then or not.
(The clause with whether modifies call.)
On the other hand, according to the Times Manual, or
not may be omitted when the word whether introduces
a noun clause used as the subject, object, or object of a preposition.
Remember that a noun clause functions as a noun and, theoretically,
can have a pronoun or a noun phrase as a substitute: this,
this fact, that, it, and
this idea, for example. If its possible to make a substitution
with a word like this or it or this
idea, or not is not necessary to the sentence.
Here are some examples of sentences in which you may omit or
not. Note that you can also include or not,
and note, too, that or not can go at the end of the
As subject of the sentence. "Whether (or
not) he leaves" is the noun clause as subject. (You could
also say: "This is of absolutely no importance
(a) Whether or not he leaves is of absolutely
no importance to me.
(b) Whether he leaves or not
is or absolutely no importance to me.
(c) Whether he leaves or stays is of absolutely
no importance to me.
If the words or not are omitted, there will
probably be a statement of alternatives connected by or,
as in this case "leaves or stays." When the words
or not are optional, their use emphasizes the
idea that there is a choice.
As a noun clause as object of the verb. In the sentences below,
wonder is the verb. Whether
(or not) hell get the job is the
noun clause. (You could also say: Brad wonders this.)
(d) Brad wonders whether hell get the
(e) Brad wonders whether or not hell
get the job.
(f) Brad wonders whether hell get the
job or not.
Informally, if is often substituted for whether,
as in (d) and (f), but not (e).
So, in answer to your question, with the example sentences
As the object of the preposition. In the sentences below, on
is the preposition. Whether (or
not) Alice wants to make the investment is the
noun clause. (You could also say: The decision depends on
(g) The decision depends on whether Alice wants
to make the investment.
(h) The decision depends on whether or not Alice
wants to make the investment.
(i) The decision depends on whether Alice wants
to make the investment or not.
If cannot be substituted in these sentences.
I asked him whether or not I should go.
I asked him whether I should go.
both whether and whether or not are
fine, since they appear at the beginning of a noun clause used as the
object of the verb asked. The entire noun clause"whether
(or not) I should go"could be substituted with
this: "I asked him this."