Directions : Study the following information carefully and answer the…

In these symbol-coded family puzzles, every operator fixes two things at once: the relationship AND the gender of the person on the left of the symbol. '@', '^', '÷' and '%' always mark a MALE person (son, father, brother, husband); '+', '-' and '=' always mark a FEMALE person (daughter, mother, sister). A chain such as 'X#Y#Z' is decoded pair by pair through the shared middle letter, and a blank inside such a chain must be filled with the ONE operator whose relationship AND gender both match what the required statement needs -- and, just as importantly, that operator must actually connect the SAME two people named in the target statement.

1. Clause 1, 'A^E+D', decodes to: A is the father of E, and E is the daughter of D -- this sentence involves only A, D and E.

2. Clause 2 up to the blank, 'L+G': L is the daughter of G, so G is a parent of L (G's own gender is not fixed by this alone).

3. 'M÷L': M is the brother of L, so M is male and shares the same parent as L -- meaning G is a parent of M as well. The blank fixes G's specific relation to M.

4. Crucially, E never appears in clause 2, and G/L/M never appear in clause 1 -- the expression gives no shared letter and no marriage ('%') link between E and G, L, or M.

5. So no matter what fills the blank, the result only fixes G's relation to M; it can never, by itself, establish 'E is the mother of M', since E and M are never connected by the expression at all.

6. Even setting that aside, the one symbol that would make G specifically the MOTHER of M is the operator defined at the start as 'is the mother of', namely '-' -- and '-' is not one of the four symbols offered here (@, +, ^, =), which give only son-of, daughter-of, father-of and sister-of.

• '@' (son of) would make G the son of M -- this reverses the parent-child direction already fixed in the steps above.

• '+' (daughter of) would also make G the child of M, the wrong direction, even though it keeps G female.

• '^' (father of) keeps G correctly as the parent of M, but fixes G as male -- the opposite gender to 'mother'.

• '=' (sister of) would make G and M siblings, contradicting the parent role G already has.

Since the expression never links E to G, L or M, and even the best-fitting symbol for making some parent 'the mother' of M ('-') is not among the four offered options, no choice among @, +, ^, = can make 'E is the mother of M' true -- the answer is 'None of these'.