4. Consider \( \mathrm{W}=\{(p, q) \mid p+q=1\} \) with the following definitions of vector addition and scalar multiplication:
\[
(p, q) \oplus(r, s)=(p+r-1, q+s) \quad c \otimes(p, q)=(c p-c+1, c q)
\]
Verify that \( \mathrm{W} \) with these two operations forms a vector space.