A text book's proof
Oh! I think it's right now! Bt, i don't get the inplies sign mean from initial. Please, discuss it in Math Club. Thanks!
A man is not finished when he's defeated, he's finished when he quits.
Re: A text book's proof
Oh fine it's very needed to me.
\[\left(\frac{a}{b}\right)^2\]
\[\left(\frac{a}{b}\right)^2\]
A man is not finished when he's defeated, he's finished when he quits.
Re: A text book's proof
actually the $=$ sign was the correct one. Now, your proof is wrong; in fact it does not make any sense at all. Saying that $A \Rightarrow B$ does not mean anything if A and B are sets.
The correct proof is the one you wrote originally :
\[A\cup (B\cap C)\]
\[= \{x:x\in A\text{ or }x\in (B\cap C)\}\]
\[= \{x:x\in A\text{ or }(x\in B\text{ and }x\in C)\}\]
\[= \{x:(x\in A\text{ or }x\in B)\text{ and }(x\in A or x\in C)\}\]
\[= \{x:x\in A\cup B\text{ and }x\in A\cup C\}\]
\[= \{x:x\in (A\cup B)\cap(A\cup C)\}\]
\[= (A\cup B)\cap (A\cup C)\]
\[[proved]\]
The correct proof is the one you wrote originally :
\[A\cup (B\cap C)\]
\[= \{x:x\in A\text{ or }x\in (B\cap C)\}\]
\[= \{x:x\in A\text{ or }(x\in B\text{ and }x\in C)\}\]
\[= \{x:(x\in A\text{ or }x\in B)\text{ and }(x\in A or x\in C)\}\]
\[= \{x:x\in A\cup B\text{ and }x\in A\cup C\}\]
\[= \{x:x\in (A\cup B)\cap(A\cup C)\}\]
\[= (A\cup B)\cap (A\cup C)\]
\[[proved]\]
Re: A text book's proof
I also think it would be =
in first i wrote =, bt, after zubaer vai's cmnt i changed it.
in first i wrote =, bt, after zubaer vai's cmnt i changed it.
A man is not finished when he's defeated, he's finished when he quits.
Re: A text book's proof
Ok, I have corrected your original post to the original post. 
Re: A text book's proof
Thanks!
A man is not finished when he's defeated, he's finished when he quits.
Re: A text book's proof
There is a typo in the 2nd line
Re: A text book's proof
Corrected