设A={a,b},B={α,β,γ},C={1,2},求A×B,B×A,A×A,(A×B)×C,A×(B×C).
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【答案】:A×B={〈α,α〉,〈α,β〉,〈α,γ〉,〈b,α〉,〈b,β〉,〈b,γ〉}.
B×A={〈α,a〉,〈α,b〉,〈β,α〉,〈β,b〉,〈γ,α〉,〈γ,b〉}.
A×A={〈a,a〉,〈a,b〉,〈b,a〉,〈b,b〉}.
(A×B)×C={〈a,α,1〉,〈a,α,2〉,〈a,β,1〉,〈a,β,2〉,〈a,γ,1〉,〈a,γ,2〉,〈b,α,1〉,〈b,α,2〉,〈b,β,1〉,〈b,β,2〉,〈b,γ,1〉,〈b,γ,2〉}.
A×(B×C)={〈a,α,1〉,〈a,α,2〉,〈a,β,1〉,〈a,β,2〉,〈a,γ,1〉,〈a,γ,2〉,〈b,α,1〉,〈b,α,2〉,〈b,β,1〉,〈b,β,2〉,〈b,γ,1〉,〈b,γ,2〉}.
B×A={〈α,a〉,〈α,b〉,〈β,α〉,〈β,b〉,〈γ,α〉,〈γ,b〉}.
A×A={〈a,a〉,〈a,b〉,〈b,a〉,〈b,b〉}.
(A×B)×C={〈a,α,1〉,〈a,α,2〉,〈a,β,1〉,〈a,β,2〉,〈a,γ,1〉,〈a,γ,2〉,〈b,α,1〉,〈b,α,2〉,〈b,β,1〉,〈b,β,2〉,〈b,γ,1〉,〈b,γ,2〉}.
A×(B×C)={〈a,α,1〉,〈a,α,2〉,〈a,β,1〉,〈a,β,2〉,〈a,γ,1〉,〈a,γ,2〉,〈b,α,1〉,〈b,α,2〉,〈b,β,1〉,〈b,β,2〉,〈b,γ,1〉,〈b,γ,2〉}.
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