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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