1) a)
“ new york state” and ( “death penalty or capital punishment”) 26 hits

b)
(“new york state and “death penalty”) or “capital punishment” 371 hits

c)
“new york state” and “death penalty” or “capital punishment” 371 hits

d)
(“new york state” and “death penalty”) or (“new york state” and “capital punishment”) 26 hits

2) a and d showed the same results . “ NYS” and “death penalty” or “capital punishment” means the exact same thing as “NYS” and “death penalty” or “NYS” and “capital punishment”. The first is just a simpler way to state it.
b and c had the same results. Whether using brackets or not these statements are the same.

3)
a) corresponds with the c) Venn diagram.
b) corresponds with the d) Venn diagram.
c) corresponds with the d) Venn diagram.
d) corresponds with the c) Venn diagram.