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Question Number 4733 by Yozzii last updated on 02/Mar/16

Commented by Yozzii last updated on 02/Mar/16

$$Howcanyoushowthat$$$$(\cup S)\times (\cup T)⊉\cup \{X\times Y\mid X\in S,Y\in T\}?$$

Commented by prakash jain last updated on 02/Mar/16

$$\mathrm{From}\mathrm{the}\mathrm{problem}\mathrm{description}\mathrm{second}\mathrm{part}$$$$\mathrm{along}\mathrm{with}\mathrm{first}\mathrm{part}\mathrm{it}\mathrm{looks}\mathrm{like}\mathrm{common}$$$$\mathrm{elements}\mathrm{in}\mathrm{elements}\mathrm{of}S\mathrm{and}T\mathrm{create}$$$$\mathrm{extra}\mathrm{element}\mathrm{in}\mathrm{RHS}.$$$$\mathrm{I}\mathrm{am}\mathrm{not}\mathrm{yet}\mathrm{able}\mathrm{to}\mathrm{identify}\mathrm{an}\mathrm{element}\mathrm{in}$$$$\mathrm{RHS}\mathrm{which}\mathrm{is}\mathrm{not}\mathrm{an}\mathrm{element}\mathrm{in}\mathrm{LHS}.$$

Commented by Yozzii last updated on 02/Mar/16

$$Somespecialcounter-example$$$$needstobefoundIthink.$$

Commented by prakash jain last updated on 02/Mar/16

$$\mathrm{To}\mathrm{me}\mathrm{they}\mathrm{appear}\mathrm{equal}.$$$$\mathrm{LHS}=\mathrm{A}$$$$\mathrm{RHS}=\mathrm{B}$$$$(x,y)\in \mathrm{B}\Rightarrow x\in X\mathrm{for}\mathrm{some}\mathrm{X}\in \mathrm{S},y\in \mathrm{Y}\mathrm{for}\mathrm{some}\mathrm{Y}\in \mathrm{T}$$$$\Rightarrow x\in (\cup \mathrm{S})\mathrm{and}y\in (\cup \mathrm{T})\Rightarrow (x,y)\in \mathrm{A}$$$$\mathrm{The}\mathrm{question}\mathrm{is}\mathrm{asking}\mathrm{that}$$$$\mathrm{\exists }(x,y)\in B\mathrm{such}\mathrm{that}(x,y)\notin \mathrm{A}.$$

Commented by Yozzii last updated on 02/Mar/16

$$ExactlywhatIthought.I{can}^{\prime }t$$$$seehowthey{can}^{\prime }tbeequalgenerally.$$

Commented by prakash jain last updated on 04/Mar/16

$$\mathrm{Did}\mathrm{you}\mathrm{find}\mathrm{a}\mathrm{counter}\mathrm{example}?$$$$123456,\mathrm{what}\mathrm{is}\mathrm{your}\mathrm{opinion}?$$

Commented by 123456 last updated on 04/Mar/16

$$\mathrm{what}(\cup \mathrm{A})\mathrm{mean}?$$

Commented by Yozzii last updated on 04/Mar/16

$$ForthesetAcontainingthesets{X}_i(1⩽i⩽n)$$$$\cup Aistheunionofall{X}_i,or$$$$\cup A=\underset{i=1}{\stackrel{n}{\cup }}{X}_i=X_1\cup X_2\cup X_3\cup ...\cup X_{n-1}\cup X_n.$$

Commented by 123456 last updated on 04/Mar/16

$$\mathrm{so}$$$$(\cup S)\times (\cup T)=\left(\underset{i=1}{\stackrel{n}{\cup }}{S}_i\right)\times \left(\underset{i=1}{\stackrel{m}{\cup }}{T}_i\right)$$$$?$$

Commented by Yozzii last updated on 04/Mar/16

$$\cup S=\underset{i=1}{\stackrel{n}{\cup }}{X}_{i}and\cup T=\underset{i=1}{\stackrel{m}{\cup }}{Y}_i$$$$sincetherighthadsidehasX\in S$$$$andY\in T.XandYarejustused$$$$toindicatethatsomememberofSand$$$$TarecrossedsuchthatX\times Y.$$$$$$

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