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In each of the following questions, say which of the answers best characterizes a result of applying resolution to the clauses shown.
| 1. | {p(x,f(x)), q(x)} and {¬p(a,y), r(y)} | |
| | {q(x), r(y)} | |
| | {q(a), r(f(x))} | |
| | {q(a), r(f(a))} | |
| | There are no resolvents. | |
| |
| 2. | {p(x,b), q(x)} and {¬p(a,x), r(x)} | |
| | {q(x), r(y)} | |
| | {q(b), r(a)} | |
| | {q(a), r(b)} | |
| | There are no resolvents. | |
| |
| 3. | {p(x), p(a), q(x)} and {¬p(y), r(y)} | |
| | {p(x), q(x), r(x)} |
| | {p(a), q(x), r(x)} |
| | {p(a), q(a), r(a)} |
| | There are no resolvents. |
| |
| 4. | {p(x), p(a), q(x)} and {¬p(y), r(y)} | |
| | {q(x), r(x)} |
| | {q(x), r(a)} |
| | {q(a), r(a)} |
| | There are no resolvents. |
| |
| 5. | {p(a), q(y)} and {¬p(x), ¬q(b)} | |
| | {q(b), ¬q(b)} |
| | {q(y), ¬q(b)} |
| | {} |
| | There are no resolvents. |
| |
| 6. | {p(x), q(x,x)} and {¬q(a, f(a))} | |
| | {p(a)} |
| | {p(f(a))} |
| | {p(a), p(f(a))} |
| | There are no resolvents. |
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