Which one of the following predicate formulae is NOT logically valid?

Note that W is a predicate formula without any free occurrence of x.

The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is _______.

For n > 2, let a {0, 1}ⁿ be a non-zero vector. Suppose that x is chosen uniformly at random from {0, 1}ⁿ.
Then, the probability that $$\sum\limits_{i = 1}^n {{a_i}{x_i}} $$ is an odd number is _______.

Graph G is obtained by adding vertex s to K_3,4 and making s adjacent to every vertex of K_3,4. The minimum number of colours required to edge-colour G is _____.