Assume we have two relations R$($a$,$b$)$ and S$($b$,$c$).$ All three attributes $($a$,$ b$,$ and c$)$ are integer attributes. Assume that Relation R contains the following tuples: $(1,2),(2,3),$ and $(3,4).$ Assume that Relation S contains the following tuples $(2,2),(2,3),(4,6)$ and $(7,1).$

R

a b

$12$

$23$

$34$

S

b c

$22$

$23$

$46$

$71$

a$)$ Give an example of an attribute $($or a combination of attributes$)$ that cannot be a primary key for relation S$,$ why? $(4$ Points$)$

c$)$ How many tuples are in the result of Natural Join between R and S$?(1$ point$)$

d$)$ Show the output of the following query $(2$ points$)$

SELECT a

FROM R$,$S

WHERE R$.$b $=$ S$.$b and S$.$c $>2$