Q6) Clearly, "∼" is not transitive.
(As y∼z and x∼z but x≻y)
Lets, look at transitivity of "≻".
To show: If x≻y & y≻z implies x≻z.
But, the antecedant is false as we're just given only one pair of strict preference relation(x≻y) and we need atleast two pairs of strict preference relation to reach some conclusion. So, the statement holds trivially.
Hence, "≻" is transitive.
:)