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The true and false proposition of discrete mathematics in freshman year. Thank you!
(1) is false. If a = {1}, b = {2}, c = {3}, then

a ∨( b×C)= { 1,& lt2,3 >},(A∪B)×(A∪C)= { & lt; 1, 1 & gt; ,& lt 1,3 & gt; ,& lt2, 1 & gt; ,& lt2,3 >}

Therefore, it will not wait.

(2) It is true.

Proof: Let any ordinal number pair

& ltx,y & gt∈A×(B∩C)

(x∈A)∧(y∈B∩C)

(x∈A)∧(y∈B∧y∈C)

(x∈A∧y∈B)∧(x∈A∧y∈C)

& ltx,y & gt∈a×B∧& lt; x,y & gt∈A×C

& ltx,y & gt∈(A×B)∩(A×C)

Therefore, A×(B∩C)=(A×B)∩(A×C).