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For each of the following pairs of expressions, say which substitution, if any, is a most general unifier.
| (a) | p(X,X) and p(a,Y) | |
| | {X←a} | |
| | {Y←a} | |
| | {X←a, Y←a} | |
| | Not unifiable | |
| |
| (b) | p(X,X) and p(f(Y),Z) | |
| | {X←f(a), Y←a, z←f(a)} | |
| | {X←f(Y), z←f(Y)} | |
| | {X←f(Y)} | |
| | Not unifiable | |
| |
| (c) | p(X,X) and p(f(Y),Y)| | |
| | {X←f(a), Y←a} | |
| | {X←f(Y), Y←f(Y)} | |
| | {X←f(Y)} | |
| | Not unifiable | |
| |
| (d) | p(f(X,Y),g(Z,Z)) and p(f(f(W,Z),V),W) | |
| | {X←W, Y←Z, W←g(Z,Z)} | |
| | {X←f(f(W,Z),V), Y←V, W←g(Z,Z)} | |
| | {X←f(g(Z,Z),Z), Y←V, W←g(Z,Z)} | |
| | Not unifiable | |
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