I'm having trouble understanding this question. Taken from Richard Jeffrey's book "Formal Logic" (4ed).
Who Am I? (Find a snappy conclusion that closes the [truth] tree).
a) $ \forall x Lxb, \forall x (Lbx \rightarrow Ixa).$ ("Ixa," x is me.)
b) $ \forall x(Bbx \rightarrow Ixa), Bbc$. ("B," begat; "a," me; "b," my father; "c," that man's father).
I know that I have to make up my own conclusion that will close all paths of the tree, but I'm having trouble understanding what the latter part of each sub question means.
I don't know what $L$ means, so I'll concentrate on (b). The second sentence of (b), $Bbc$, just states "$b$ begat $c$", or in other words "my father begat that man's father". The first sentence is a little harder: $\forall x(Bbx \rightarrow Ixa)$. Read it in stages. First, we can translate the "$\forall x$": "for every $x$, $Bbx \rightarrow Ixa$". Next, translate the $\rightarrow$: "for every $x$, if $Bbx$ then $Ixa$". Translate the predicates: "for every $x$, if $b$ begat $x$ then $x$ is $a$". And finally, translate the constants: "for every $x$, if my father begat $x$, then $x$ is me."
The next step is to rephrase it in a way that's more natural, ideally without variables. So we have "For any person, if my father begat that person, then that person is me." Better: "Any person my father begat is me". Still a little awkward, so we can make it better: "The only person my father begat is me". Or even better: "I am my father's only child."
So we know "I am my father's only child" and that "my father begat that man's father". What's the immediate consequence?