First order predicate logic for "Every bike is a two wheeler manufactured by Hero".

Question

Let

$A(x)=x$ is a two wheeler

$B(x)=x$ is a bike

$C(x)=x$ is manufactured by hero.

Which of the following is first order predicate logic for statement

Every bike is a two wheeler manufactured by Hero.

1. $∀x(A(x)\land B(x))→C(x)$
2. $∀x(A(x)→ B(x))→C(x)$
3. $∃ x(A(x)\land B(x))→C(x)$
4. $∃ x(A(x)→ B(x))→C(x)$

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My attempt:

Given statement can be written as following:

If $x$ is a two wheeler then it is a bike then $x$ is manufactured by Hero

Therefore,

$$∀x(A(x)→ B(x))→C(x)$$

Can you explain in formal way, please?

Answer 1

None of the options is correct. Your reformulation "If $x$ is a two wheeler then it is a bike then $x$ is manufactured by Hero" is also not correct.

The statement can be reformulated as "If $x$ is a bike, then $x$ is a two-wheeler and $x$ is manufactured by Hero", which in formal terms is $\forall x (B(x)\to(A(x)\land C(x))$. None of the options given is equivalent to this statement.