Relations between statements involving universal quantifier, conditional and biconditional

Question

If we consider two predicates:

$b(x)$: x is a boy

$c(x)$: x is clever

Then, there are four statements involving $∀, b(x), c(x), →$ and $↔$ . These are below along with my interpretation of their meaning. Correct me if I am wrong in any of these interpretations.

(a) $∀x(b(x)→c(x))$ - All boys are clever

(b) $∀x(b(x))→∀x(c(x))$ - If all are boys, then all are clever

(c) $∀x(b(x)↔c(x))$ - All boys are clever & all those who are clever are boys

(d) $∀x(b(x))↔∀x(c(x))$ - If all are boys, then all are clever & if all are clever then all are boys

I am trying to determine all conditional $(→,↛)$ / bi-conditional $(↔)$ relations between each two of above four. Between any two of these, if there is $↔$, then there is only one relation. However, if there is conditional relation in one direction, then conditional relation in other direction will be invalid. That is there can be $(→,↛)$. So at max there will be $4C_2\times 2=12$ such relations.

Now to understand these relations, I prepared below table. I considered that there are only two person in the universe $x_1,x_2$. $\{(b,c),(¬b,¬c)\}$ means $x_1$ is boy and is clever and $x_2$ is not a boy and is not clever. The truth values (in table) in boldface (all other than vi, viii and xiv) are one which I feel are correct, though I am not sure. The non bold-faced truth values (vi, viii and xiv) are ones which I am unsure. So, I am more likely make mistake with them.

Based on the truth values in above table, I prepared following relations:

Q. Are relations 1 to 12 correct?

Q. Also is there some fault in the example predicates $b(x)$ and $c(x)$ themselves?

Actually, I must doing similar for existential quantifier. But afterwards. But am I correct with all this thinking or am just over thinking? Or am severly screwed with my logics?