Consider the square root of 1000. The largest prime less than this is 31. So the set of all prime numbers less than or equal to 31 i.e., { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31} must be represented in set A.

The above set itself cannot be set A, as the members of set A are non-prime.

Therefore, each member of set A must represent exactly one of these prime numbers as, set A is such that maximum number of elements. If, any member of the set is a combination of 2 or more primes from the above set, then the number of elements in set A will get reduced as the members of this set should be co-prime to each other.

Set A could be  {22, 32, 52, 112, 132, 172, 192, 232, 292, 312,}

It can be noted that there are more possibilities for set A. A number of set A could t, a product of exactly one prime number from the original set and another prime number which is not from the original set.

If  none of the prime numbers is used on more than one occasion then the set of numbers will be co-primes and hence satisfy the coordination for set A.

Each member must represent one prime number from the original set.

    ∴ There are exactly 11 elements.   

We get a = 4, c = 2, e = 6; b = c + a = 6 + 4 = 10 and b – d = d is given by 10 – 5 = 5.

The party (even or odd) of the expression will be the same as that of the sum of the first n natural numbers. Hence we need to check the party of n(n + 1)/2 n(n + 1)/2 is certainly even only when n is a multiple of 4 and for no other statement can a definite conclusion be drawn. so Malini wins if n is a multiple of 4.