5.2 One for all. 1-IN-3 SAT is a variant of 3-SAT where each clause is satisfied if exactly one of its literals is true. Prove that 1-IN-3 SAT is NP-complete. In fact, prove that the special case POSITIVE 1-IN-3 SAT, where no variables are negated, is NP-complete. First, make a judicious choice of which NP-complete problem would be easiest to re- duce from 5.2 One for all. 1-IN-3 SAT is a variant of 3-SAT where each clause is satisfied if exactly one of its literals is true. Prove that 1-IN-3 SAT is NP-complete. In fact, prove that the special case POSITIVE 1-IN-3 SAT, where no variables are negated, is NP-complete. First, make a judicious choice of which NP-complete problem would be easiest to re- duce from