To show that the set of clauses {{C, ¬C, A}, {C, ¬A}, {¬B, ¬A}, {¬B, C}, {¬C}, {A, B}} is unsatisfiable, we can use the resolution method.

First, we write out all possible pairs of clauses:

From {C, ¬C, A} and {C, ¬A}: We can resolve on C to obtain {¬A, A}, which can be simplified to the empty clause {}.
From {¬B, ¬A} and {¬B, C}: We can resolve on ¬B to obtain {¬A, C}, which can be simplified to {¬A, C}.
From {¬C} and {¬A, C}: We can resolve on C to obtain {¬A}, which can be simplified to {¬A}.
From {A, B} and {¬A}: We can resolve on A to obtain {B}, which cannot be further simplified.
At this point, we have obtained the empty clause {}, which indicates that the set of clauses is unsatisfiable. Therefore, there is no truth assignment that satisfies all the clauses, and the set of clauses is contradictory.
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