First order predicate logic for "Every bike is a two wheeler manufactured by Hero". 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. $∃ x(A(x)→ B(x))→C(x)$ * * * 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?

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.