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Wolf’s A Mathematical Tour Through Mathematical Logic, Section 1.3, Exercise 5:

Exercise 5. Translate the following statements into symbolic form, as in the previous example.

(a) All crows are black, but not all black things are crows.
(b) If everybody complains, no one will get help.
(c) Everybody loves somebody sometime.

My attempt at (a): Let $C(x)$ be the statement “$x$ is a crow”, where $x$ is the variable whose domain is all the things, living or non living.
Let $B(x)$ be the statement “$x$ is black”, where $x$ has the same domain as above.
So I think it should translate as $$\forall x(C(x)\rightarrow B(x)).$$

Is it correct?

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Atom
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    Your formula is the correct transaltion of "All crows are black". – Mauro ALLEGRANZA Jun 06 '19 at 10:35
  • How do you answer (c)? – x.projekt Jul 02 '20 at 18:51
  • @harshatech2012 I’d translate it like this. Let $P(x,y, t)$ be the statement that “$x$ loves $y$ at time $t$” where $x,y$ range over all the humans and $t$ ranges over time. Then I’d write $\forall x\exists y\exists t P(x,y,t)$. – Atom Jul 03 '20 at 05:42
  • @Atom Yes, it's a possible solution. See this question for more answers: https://math.stackexchange.com/q/3742919/493216 – x.projekt Jul 03 '20 at 07:02

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Your answer is partially correct since you did not translate "but not all black things are crows" part. You first can interpret it as "there is a black thing that is not a crow" and translate it as $$\exists x(B(x) \land \lnot C(x))$$

Now, can you connect this with your answer?

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