【数学简单证明英语LetA,B,C,andDbenonemptysets.ThenA×B=C×DifandonlyifA=CandB=D.(a)Provethisstatement.(b)Oneofthetwoimplicationsdoesnotrequirethesetstobenonempty.Whichone?(c)Ifwedonotrequirethesetsto】
数学简单证明英语
LetA,B,C,andDbenonemptysets.ThenA×B=C×DifandonlyifA=CandB=D.
(a)Provethisstatement.
(b)Oneofthetwoimplicationsdoesnotrequirethesetstobenonempty.Whichone?
(c)Ifwedonotrequirethesetstobononempty,thenthestatementisfalse.GiveexamplesofsetsA,B,CandDtoshowthenecessityoftheassumptionthatthesetsbenonempty.