টেমপ্লেট:রঙিন অনুশীলন

অনুশীলন. {ধরুন $a$ এবং $b$ দুটি ভিন্ন উপাদান। নিম্নোক্ত প্রতিটি বাক্য কি সত্য নাকি মিথ্যা?

১. এই সেট {{}} - True. + False. || This set contains one element, namely the empty set $\{\}$.

{$\{\}=\varnothing .$ |type="()"} + True. || These two sets have no elements, thus containing the "same" elements. - False.

{$\{1,1,2,3\}$ is a set. |type="()"} + True. || Even if the element "1" is listed two times, it still represents a set (which can also be denoted by $\{1,2,3\}$). - False.

{$\{x:0<x<2\text{ and }{x}^2=4\}=\{2\}$. |type="()"} - True. + False. || Solving $x^2=4$, we get $x=\pm 2$, but both of them are not between 0 and 2 exclusively, so no $x$ satisfies the given property. As a result, the set on the RHS should be empty. }

{$\{a,b,b\}\in \{\{a,b\},a,b,b\}$. |type="()"} + True. || First, $\{a,b,b\}=\{a,b\}$. Since the set $\{a,b\}$ is an element of the set on RHS, this is true. - False.

{$\{\{a\},\{a\}\}\in \{\varnothing ,\{a\},\{b\},\{a,b\}\}$. |type="()"} - True. + False. || First, $\{\{a\},\{a\}\}=\{\{a\}\}$. But set $\{\varnothing ,\{a\},\{b\},\{a,b\}\}$ doesn't contains $\{\{a\}\}$, it only contains $\{a\}$, which is not the same. </quiz> }} }

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