A useful formula for agenda planning

Consider 5 boolean variables x1, x2, x3, x4, x5

a) Write a propositional formula which expresses the fact that one and at most one among the Boolean variables x1, x2, x3, x4, x5 is true.

b) Compute a conjunctive normal form of this formula, your answer must be justified. For instance, you can apply the function CNF seen in class. CNF from class:

1 CNF(p) = p 2 CNF(p) = p

3 CNF(? ? ?) = CNF(?)?CNF(?) 4 CNF(???) = CNF(?)?CNF(?) 5 CNF(? ? ?) = CNF(?)?CNF(?) 6 CNF(? ? ?) = CNF(? ? ?)?CNF(? ? ?) 7 CNF(?) = CNF(?) 8 CNF((? ? ?)) = CNF(?)?CNF(?) 9 CNF((???)) = CNF(?)?CNF(?) 10 CNF((? ? ?)) = CNF(?)?CNF(?) 11 CNF((? ? ?) = CNF(???)?CNF(???)