From No A are B and No B are C, which of the following can be concluded?

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Multiple Choice

From No A are B and No B are C, which of the following can be concluded?

Explanation:
Disjointness relations like “No A are B” and “No B are C” do not force a definite relationship between A and C. All you know is that A shares nothing with B, and B shares nothing with C; that tells you nothing about A and C themselves. So you cannot conclude any fixed relation between A and C. For example, choose A = {1}, B = {2}, C = {1}. This satisfies both premises because A and B are disjoint, and B and C are disjoint, yet A and C share the element 1, so “No A are C” is false in this case. But if you instead choose A = {1}, B = {2}, C = {3}, then A and C are disjoint, making “No A are C” true in that scenario. Since either outcome is possible, the only safe conclusion is that nothing definite can be concluded about A relative to C.

Disjointness relations like “No A are B” and “No B are C” do not force a definite relationship between A and C. All you know is that A shares nothing with B, and B shares nothing with C; that tells you nothing about A and C themselves. So you cannot conclude any fixed relation between A and C.

For example, choose A = {1}, B = {2}, C = {1}. This satisfies both premises because A and B are disjoint, and B and C are disjoint, yet A and C share the element 1, so “No A are C” is false in this case. But if you instead choose A = {1}, B = {2}, C = {3}, then A and C are disjoint, making “No A are C” true in that scenario. Since either outcome is possible, the only safe conclusion is that nothing definite can be concluded about A relative to C.

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