1. All Kenyans are Africans. Hence, no Kenyans are non-Africans.

前提：All Kenyans are Africans

結論：No Kenyans are non-Africans

結論「No Kenyans are non-Africans」是前提「All Kenyans are Africans」的質述反轉(Obversion)

當前提質述反轉時，主詞、述詞不改變？且不換位，量詞也不變，但質會變成否定的(即non)。此題我們可以由前提推出結論：

述詞有改變啊！

All Kenyans are Africans（前提）

↓

No Kenyans are not Africans

↓

No Kenyans are non-Africans（結論）

因此就會如圖所示一般，是兩個相同的圖，故這是屬於「有效論證」

由於這是屬於「質述反轉」，所以不論在存在觀點下或假設觀點下，此論證都是屬於「有效論證」不是因為它是質述反轉的關係，是因為它是由A語句轉變成E語句，而非由全稱語句轉變成偏稱語句的關係。

8. Some stars are not luminous bodies. So some luminous bodies are not stars.

前提：Some stars are not luminous bodies

結論：Some luminous bodies are not stars

結論「Some luminous bodies are not stars」是前提「Some stars are not luminous bodies」的位反轉(conversion)

當前提位反轉時，主詞、述詞換位，但量詞不變。因為這是屬於O語句的位反轉，它們在邏輯上是彼此獨立的，即不等值且不能推出對方，因此就會如圖所示一般，是兩個不同的圖，因為由前提無法推出結論，故是屬於「無效論證」

由於這是屬於O語句的位反轉(conversion)，所以不論在存在觀點下或假設觀點下，此論證都是屬於「無效論證」

O語句是偏稱否定語句，既說「有星星不是發光體」，那說者便預設了有星星的存在。因此這個論證不會是從假設觀點談，一定是存在觀點。

B. By what sequence of steps can the second sentence be validly inferred from the first? Operations of immediate inference and relationships from the square of opposition may be used. Make clear any existential presuppositions.

1. No Africans are Buddhists. Some Africans are non-Buddhists.

直接推論：

No Africans are Buddhists.

(定言語句形式：No S are P)

質述反轉(Obversion)：All Africans are non-Buddhists.

(定言語句形式："No S are P" is equivalent to "All S are nonP")

加限的位反轉(Conversion by limitation)：Some non-Buddhists are Africans.

(定言語句形式："All S are P" implies "Some P are S")

「加限的位反轉有預設至少有Africans的存在，否則無法使用；其他不管有無預設Africans的存在，皆可做等值轉換」別學我

質述反轉(Obversion)：Some non-Buddhists are not non-Africans.

(定言語句形式："Some S are P" is equivalent to "Some S are not nonP")

位詞反轉(Contraposition)：Some Africans are not Buddhists.

(定言語句形式："Some S are not P" is equivalent to "Some nonP are not nonS")

質述反轉(Obversion)：Some Africans are non-Buddhists.

(定言語句形式："Some S are not P" is equivalent to "Some S are nonP)

推論步驟如下：

No Africans are Buddhists.(前提)

↓質述反轉

All Africans are non-Buddhists.

↓加限的位反轉

Some non-Buddhists are Africans.

↓質述反轉

Some non-Buddhists are not non-Africans.

↓位詞反轉

Some Africans are not Buddhists.

↓質述反轉

Some Africans are non-Buddhists.(結論)

C. Explain why each argument is not valid.

3. All bureaucrats are officials. So all officials are bureaucrats.

前提：All bureaucrats are officials

結論：All officials are bureaucrats

結論「All officials are bureaucrats」是前提「All bureaucrats are officials」的位反轉(conversion)

如范恩圖所示，雖然前提與結論皆為A語句，但它們的位反轉在邏輯上是彼此獨立的，即不等值因此不能從前提推出結論，因此可知這是屬於「無效論證」