Determine wether or the following subsets are subspaces of F

[lonewolf999]

Homework Statement

Let F be the vector space (over R) of all functions f : R−R. Determine whether or not the following subsets of F are subspaces of F:

Homework Equations

1. S1 = {f e F|f(−3) = 0 and f(10) = 0};
2. S2 = {f e F|f(−3) = 0 or f(10) = 0}.

The Attempt at a Solution

I know how to do questions of this nature however i am confused with how to go about solving these two due to the "and", "or" that have been put into the equation.

Can i assume that in equation 1 if f(−3) = 0 and f(10) = 0 then i can write f(−3) + f(10) = 0, if this is correct how do i go about solving the equation in 2.

 

[tiny-tim]

hi lonewolf999!

Let F be the vector space (over R) of all functions f : R−R. Determine whether or not the following subsets of F are subspaces of F:
…
Can i assume that in equation 1 if f(−3) = 0 and f(10) = 0 then i can write f(−3) + f(10) = 0 …

nooo, you're losing the plot

the plot is about vector spaces, and nothing matters except the definition of a vector space (and your f(−3) + f(10) has nothing to do with that)

multiplication by a scalar obviously isn't a problem, so the main worry is whether f+g is in F if both f and g are …

try that ​