E15C-10.(E&F) ⊃G, H⊃E, ∴F⊃(H⊃G)

B-1

C ⊃D, D ∴C

設此論證為前提真且結論假的無效論證，因此設D為真，而C為假。當D為真且C為假時，C⊃D可為真。因此可知當D真C假時，整個論證無效。因此這個論證是無效論證。

C-3 If either revenues increase or debt and costs decrease, the firm's profitability will improve. Costs won't decrease unless debt decreases. It's not the case both that revenues will increase and that profitability will improve. Therefore, either debts won't decrease or profitability will improve.

Let "R" mean "Revenues increase," let "D" mean "Debt increase," let "C" mean "Costs increase," and let "F" mean "profitability will improve."

論證符號後如下：

1.      [R∨(–D&–C)] ⊃F

2.      –C⊃–D

3. –(R&F)

∴D∨F

先由short-cut method檢驗一下是否為無效論證。

由此可知，在C為真而D, F, R為假時，會有前提真而結論假的情況。所以這是個無效論證。

D-6 p⊃q, q⊃r, p&–r

導出矛盾，可知這組語句是不一致的。