Bag union operation in relational algebra
After giving this question little thoughts, I found, I was missing the projection part which means the only attribute A is considered for the union. So, basically all we have to do is grouping using GAMMA and then select attribute A and perform union.

Derivation:


\gamma(x,y,avg(z)) => {(2,6,5),(5,6,3),(9,0,4)}


renaming avg(z) to A and projecting that column results in:

{5,3,4}


Remaining 2,3 and 4 with the same method then becomes:


{11,8}
{5,1,1}
{5,9}


So we end up with the bag:

{5,3,4, 11,8, 5,1,1 ,5,9}


Clearly statement a, b and d is False and statement c is True