Question

Correct symbolical representation of statement  => "All Birds are beautiful" ?

Now , here the logical way to approach seems like necessary condition.

Since All birds are beautiful , can be equivalent to , "If X is a bird then X is beautiful."

Again , with Universal quantifier ; simply (Vx) { B(x) -> Beauty(x) } .

I observed , the answer chosen is , ~ [∃x , { B(x) ^ Beauty(x) } ] .

First , I'm totally lost now , with when to choose conjunction vs implication and how the above form is closer to sentential form.

Answer 1

Are you sure that the chosen answer wasn't: ~ [∃x , { B(x) ^ ~ Beauty(x) } ] .

Comments

Why ? ~ [∃x , { B(x) ^ ~ Beauty(x) } ]  is Equivalent to

[Vx , { ~ B(x) v Beauty(x) } ]  , right ?  

Isn't implication more intuitive here , why'd we choose conjunction to represent this sentence ?

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Yes and:
p -> q is equivalent to
~p v q

Thus, [Vx , { ~ B(x) v Beauty(x) } ] is equivalent to
[Vx , { B(x) -> Beauty(x) } ]

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It has to be misprint , it's fairly obvious ; what's going on here.

Answer 2

It should be this ~ [∃x , { B(x) ^~ Beauty(x) } ]