The problem 3-SAT and 2-SAT are
(A)
both in P
(B)
both NP complete
(C)
NP-complete and in P respectively
(D)
undecidable and NP-complete respectively
Answer: (C)
Explanation:
The Boolean satisfiability problem (SAT) is a decision problem, whose instance is a Boolean expression written using only AND, OR, NOT, variables, and parentheses.
The problem is: given the expression, is there some assignment of TRUE and FALSE values to the variables that will make the entire expression true?
A formula of propositional logic is said to be satisfactory if logical values can be assigned to its variables to make the formula true. 3-SAT and 2-SAT are special cases of k-satisfiability (k-SAT) or simply satisfiability (SAT) when each clause contains exactly k = 3 and k = 2 literals respectively. 2-SAT is P while 3-SAT is NP-Complete.
References: http://en.wikipedia.org/wiki/Boolean_satisfiability_problem
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