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 satisfiable if logical values can be assigned to its variables in a way that makes 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. (See this for explanation)

References:
http://en.wikipedia.org/wiki/Boolean_satisfiability_problem


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