First order logic - all x is y and all y is z

Question

How do I express the following in a single sentence in first order logic?

All x is y and all y is/does z

I wish to keep the individual relationships between x and y and then y and z respectively.

For example, all whales are mammals and all mammals give birth to live young.

I came up with

∀x, Whales(x) -> Mammals(x), Mammals(x) -> GiveBirthLiveYoung(x)

This seems like bad form some how as I've never seen an example with a separating comma and right arrows in a single sentence.

Answer 1

You can either do it as two sentences, or as one with a conjunction.

$$\forall x: Whales(x) \to Mammals(x) \wedge Mammals(x) \to Birth(x)$$ or

1. $\forall x: Whales(x) \to Mammals(x)$
2. $\forall x: Mammals(x) \to Birth(x)$

Answer 2

Best to use parentheses to make explicit the scope of the quantifier.

$$\forall x \big((\text{Whales}(x) \to \text{Mammals}(x)) \land (\text{Mammals}(x) \to \text{GiveBirthLiveYoung}(x))\big)$$

There is nothing incorrect or invalid about this form.