Explanation:
i)
A = {2, 3, 5, 7}
as "1" can only be divided by one number (instead of the usual 2 numbers for prime numbers), if it's not part of that set.
out of U = {1, 2, 3, 4, 5, 6, 7, 8}
B = {1, 3, 5}
I am not sure what you mean by "y E 7".
I don't think you mean the E7 algebraic group.
I decided you mean y <> 7 (not equal to 7).
ii)
A u B (united) = {1, 2, 3, 5, 7}
A n B (elements in common) = {3, 5}
iii)
a set with n elements has 2^n subsets and (2^n) - 1 proper subsets (all subsets minus the equal one).
our U here has 8 elements, so the number of subsets is
2⁸ = 256.
the number of relations from A to B is 2^|A×B| = 2^(|A|·|B|).
|A| = 4
|B| = 3
so the number of relations from A to B are
2^(4×3) = 2¹² = 4096
remember, for the number of possible relations we have 4×3 = 12 possible combinations of elements of A and engender of B.
each of these combinations can be in the set of relations or not, which gives us 2 options per combination.
that gives us 2¹² relations.