Prove or disprove:

If is a null sequence then one or both of is(are) null.

My attempt:

if both are null then certainly is null, no problem with that.

I assumed that is not null, is not null and as given, is null. I tried to bring a contradiction since i have a feeling that the statement in the question is true.

since its assumed that is not null so:

there existssuch that for allthere existssuch that

similarly:

there existssuch that for allthere existssuch that

and since is null:

there existssuch that

now since i can't say that occur at thesamei can't find a contradiction.

someone help.