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The brackets just make it clear which part of the sentence you want the "for all" quantifier to apply. In larger sentences you might want to quantify for some of the equation but not the rest. I guess in this case the brackets weren't needed.The 'v' and upsidedown 'v' you're talking about sound like the symbols for logical disjunction and conjunction , respectively. There's a Wikipedia page which includes all these symbols and describes their meaning if you're interested: http://en.wikipedia.org/wiki/List_of_ma … al_symbols (Scroll down about half way for the dis and conjunction symbols.)
When do i use the brackets and what is the meaning of the 2 signs which look like v and upsidedown v.
This could be a way to write it:
How do i write this using logic symbols "for all natural number x there exists a unique y such that y is twice as x" ? 