Answer: E

Small Hint:

Represent the comparisons as propositions and distinguish each implication from its converse

Big Hint:

The second premise’s hypothesis is incompatible with the first premise’s conclusion, but that alone does not chain the implications

Solution:

Let $P$ mean $a>b,$ $Q$ mean $c>d,$ $S$ mean $c<d,$ and $R$ mean $e>f.$ The premises are $$P\Rightarrow Q,\qquad S\Rightarrow R.$$ The statements $Q$ and $S$ cannot both hold. The contrapositives are $\neg Q\Rightarrow\neg P$ and $\neg R\Rightarrow\neg S.$ None of the four proposed implications follows. For example, knowing $P$ gives $Q$ and hence $\neg S,$ but says nothing about $R;$ knowing $\neg R$ gives $\neg S,$ not $P.$

Therefore, the correct answer is E.