Hi there I have this theorem about sub-spaces...I took it as an arbitrary theorem:
If W is a subset of one or more vectors from a vector space V, then W is a subspace of V if and only if the following conditions hold:
a) if u,v is an element of W, then (u + v) is an element of W
b) if u is an element of W and k is a scalar, then ku is an element of W
Now I want to translate this theorem into symbolic logic...my first attempt is as follows:
Let:
p: W is a subset of one or more vectors from a vector space V.
q: W is a sub-space of V
a and b will represent the conditions mentioned with their corresponding letters as variables.
My translation:
(p => q) <=> (a ^ b)
In the back of my mind though, I am thinking about why the translation can't be this:
p => [q <=> (a^b)]
Can someone please help with this? I need to know how the order of precedence works when translating from English to symbolic logic...like how would a comma before if and only if make a difference?