ПРИМЕРЫ РЕШЕНИЯ ЗАДАЧ.

Задача 1. Пусть А={1,2,3,4,5,6,7}; В={4,5,6,7,8,9,10}; С={2,4,6,8,10}; И={1,2,3,4,5,6,7,8,9,10}. Определить следующие множества: .

Решение.

АÇВ={4,5,6,7}

={1,2,3,8,9,10}.

 

Задача 2. Для множества используйте диаграммы Эйлера-Венна и заштрихуйте те ее части, которые изображают заданное множество: (АÈВÈС)\ (АÇВÇС).

Решение.

1) 2)

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А В

 

y ZXYueG1sTI9BTsMwEEX3SNzBGiQ2FbUbaDEhToUqsYFFoe0BnGRIIuxxiN3UvT3uCpZf8/T/m2Id rWETjr53pGAxF8CQatf01Co47F/vJDAfNDXaOEIFZ/SwLq+vCp037kSfOO1Cy1IJ+Vwr6EIYcs59 3aHVfu4GpHT7cqPVIcWx5c2oT6ncGp4JseJW95QWOj3gpsP6e3e0Ct62H7NzFlezn8dltYmTNPHd G6Vub+LLM7CAMfzBcNFP6lAmp8odqfHMpCzEIqEK7mUG7AI8PSyBVQqkFMDLgv//oPwFAAD//wMA UEsBAi0AFAAGAAgAAAAhALaDOJL+AAAA4QEAABMAAAAAAAAAAAAAAAAAAAAAAFtDb250ZW50X1R5 cGVzXS54bWxQSwECLQAUAAYACAAAACEAOP0h/9YAAACUAQAACwAAAAAAAAAAAAAAAAAvAQAAX3Jl bHMvLnJlbHNQSwECLQAUAAYACAAAACEAwpL7zfMBAADtAwAADgAAAAAAAAAAAAAAAAAuAgAAZHJz L2Uyb0RvYy54bWxQSwECLQAUAAYACAAAACEA00oUbd4AAAAJAQAADwAAAAAAAAAAAAAAAABNBAAA ZHJzL2Rvd25yZXYueG1sUEsFBgAAAAAEAAQA8wAAAFgFAAAAAA== " strokecolor="black [3040]"/> С С

 

3)

 

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С

Задача 3. Доказать формулу АÇ(ВÈС)=(АÇВ)È(АÇС), пользуясь принципом "Х£У и У£ХÞХ=У".

Доказательство.

Пусть Х=АÇ(ВÈС), У=(АÇВ)È(АÇС).

1. Пусть а ÎХÞ(а ÎАÇ(ВÈС))Û (а ÎА) и (а Î(ВÈС))Û а ÎА и (а ÎВ или а ÎС))Û(а ÎА) и (а ÎВ)) или ((а ÎА) и (а ÎС)) Û (а Î(АÇВ)) или (а Î(АÇС)) Û(а Î(АÇВ) È (АÇС)) Û а ÎУÞХ£У.

2. Пусть а ÎУÞ(а Î(АÇВ)È(АÇС))Û (а Î(АÇВ)) или (а Î(АÇС))Û (а ÎА) и (а ÎВ)) или (а ÎА) и ((а ÎС)Û(а ÎА) и ((а ÎВ) или (а ÎС)) Û ((а ÎА) или (а Î(ВÈС)) Û(а ÎАÇ(ВÈС))Û а ÎХÞУ£Х.

Из 1. и 2. Þ Х=У.