In a certain code language,

M & N means ‘M is the husband of N’,

M @ N means ‘M is the brother of N’,

M $ N means ‘M is the father of N’,

M # N means ‘M is the mother of N’.

Based on the above, how is F related to J if ‘F & G # H @ I $ J’?

To determine how F is related to J, we can decode the given coded expression step-by-step from left to right: ‘F & G # H @ I $ J’.

Let us define the meaning of each symbol based on the instructions:
- M & N: M is the husband of N.
- M @ N: M is the brother of N.
- M $ N: M is the father of N.
- M # N: M is the mother of N.

Now, let us analyze the relation between each adjacent pair in the expression:
1. F & G: Since ‘&’ means husband, F is the husband of G. This implies F is male, G is female, and they are married (F = husband, G = wife).
2. G # H: Since ‘#’ means mother, G is the mother of H.
3. H @ I: Since ‘@’ means brother, H is the brother of I. This means H and I are siblings, sharing the same mother G (and therefore the same father F).
4. I $ J: Since ‘$’ means father, I is the father of J. Since I is the child of F and G, J is the child of I.

Now, let us trace the relation from F to J:
- F is the husband of G, and G is the mother of H and I. Thus, F is the father of I.
- I is the father of J.
- Therefore, F is the father of J's father, which means F is the Father’s father of J.

Hence, the correct answer is Father’s father.