Consider the statement
"Not all that glitters is gold"
Predicate glitters$$(x)$$ is true if $$x$$ glitters and
predicate gold$$(x)$$ is true if $$x$$ is gold.

Which one of the following logical formulae represents the above statement?

An ordered $$n$$-tuple $$\left( {{d_1},\,\,{d_2},\,....,{d_n}} \right)$$ with $${{d_1} \ge ,\,\,{d_2} \ge .... \ge {d_n}}$$ is called graphic if there exists a simple undirected graph with $$n$$ vertices having degrees $${d_1},{d_2},.....,{d_n}$$ respectively. Which of the following $$6$$- tuples is NOT graphic?

Consider an undirectional graph $$G$$ where self-loops are not allowed. The vertex set of $$G$$ is $$\left\{ {\left( {i,j} \right):\,1 \le i \le 12,\,1 \le j \le 12} \right\}.$$ There is an edge between $$(a,b)$$ and $$(c,d)$$ if $$\left| {a - c} \right| \le 1$$ and $$\left| {b - d} \right| \le 1$$. The number of edges in this graph is _____.

Assume that there are $$3$$ page frames which are initially empty. If the page reference string is $$1, 2, 3, 4, 2, 1, 5, 3, 2, 4, 6,$$ the number of page faults using the optimal replacement policy is______________.