推 TampaBayRays:感謝你!!!! 11/15 00:21
※ 引述《TampaBayRays (坦帕灣光芒)》之銘言：
: Let A,B,C,D be sets.
: Prove (A ×B)-(C ×D)=[(A-C) ×B]∪[A ×(B-D)]
: 請各位高手幫幫我
: 謝謝
Assume (x,y) ε (A ×B)-(C ×D)
i.e. (x,y) ε (A ×B) ,and (x,y) ψ (C ×D)
(ε denotes belong to ,and ψ denotes doesn't belong to)
Iff x ε A ,and y ε B ,and (x ψ C or y ψ D)
Iff (x ε A ,and y ε B ,and x ψ C) or (x ε A ,and y ε B ,and y ψ D)
Iff (x ε A-C ,and y ε B) or (x ε A ,and y ε B-D)
Iff (x,y) ε [(A-C) ×B]∪[A ×(B-D)]
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