# Predicate Logic: Semantics and Validity

#### joyofbitz

##### New member
Hello,

Given the domain as:

D = {a,b}; ~Ba & Bb & Laa & ~Lab & Lba & ~Lbb

Why is the interpretation false? (∀x)[Bx ⊃ (Lxx ⊃ Lxa)]

I am having trouble understanding why that is the case because (Lxx ⊃ Lxa) evaluates to true in any case as long as Lxa is true in all cases, so the overall interpration should be true in all cases.

The false case that is given is: Ba ⊃ (Laa ⊃ Laa), but isn't this case true as well?

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
You are right: the formula (∀x)[Bx ⊃ (Lxx ⊃ Lxa)] is true in the given interpretation.