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This is a pseudo-sufficient assumption question.
P:All leaders in major parities oppose the bill
C:The bill will most likely fail to pass.
Target answer to connect no support with fail to pass.
Answer Choice Analysis:
A. Most bills that have not been supported by even one leader of a major party have not been passed into law
E. Most bills that have been passed into law are supported by at least one leader of a major party.
Isn't E the contrapositive of A?
http://classic.7sage.com/lsat_explanations/lsat-30-section-2-question-21/
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From my memory, I think the correct answer is A.
As for your question regarding contrapositive, watch out for quantifiers such as some and most.
Remember what the lessons taught you: there are NO contrapositives for quantified statements.