Math's Lover: Siap2 arep Quiz Analisis Real

If A and B are set, show that A $\subseteq$ B if and only if (A $\cap$ B) = A

Answer :
We will show that
A $\subseteq$ B $\rightarrow$ (A $\rightarrow$ B) = A
(i) claim (A $\cap$ B) $\subseteq$ A
let x $\in$ (A $\cap$ B)it will shown x $\in$ A
since x $\in$ (A $\cap$ B), then x $\in$ A and x $\in$ B
thus x $\in$ A
therefore (A $\cap$ B) $\subseteq$ A
(ii) Claim A $\subseteq$ (A $\cap$ B)
let x $\in$ A
it will be shown x $\in$ (A $\cap$ B)
since x $\subseteq$ A and A $\subseteq$ B then x $\in$ B
since x $\in$ A and x $\in$ B we have x $\in$ (A $\cap$ B)
therefore A $\subseteq$ (A $\cap$ B)
Since (A $\cap$ B) $\subseteq$ A and A $\subseteq$ (A $\cap$ B), we have A $\cap$ B = A ......(*)

We will show that
(A $\cap$ B) = A $\rightarrow$ A $\subseteq$ B
Claim A $\subseteq$ B
let x $\in$ A it will be shown x $\in$ B
since x $\in$ (A $\cap$ B)= A, then A $\cap$ B $\subseteq$ A
then we have x $\in$ (A $\cap$ B) and x $\in$ A
since x $\in$ (A $\cap$ B) then x $\in$ A and x $\in$ B
thus x $\in$ B
therefore A $\subseteq$ B ...... (**)

Since (*) and (**) we have A $\subseteq$ B $\leftrightarrow$ A $\cap$ B = A

woooooiii... arep nutukake ngetike kok kesyel yoooo???? hehehe

Math's Lover

Tuesday, June 21, 2011

Siap2 arep Quiz Analisis Real

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