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?

Suppose you break a stick of unit length at a point chosen uniformaly at random. Then the expected length of the shorter stick is __________________.

Four fair six-sided dice are rolled. The probability that the sum of the results being 22 is X/1296. The value of X is__________

Which one of the following propositional logic formulas is TRUE when exactly two of $$p, q,$$ and $$r$$ are TRUE?