Logic Tautology

Question

True/Flase: if a,b,c ⊨ d so at least one of this term is tautology: a→d or b→d or c→d

Maybe someone know how to proof that?

Thanks for help and have a good day!

Answer 1

If $a,b,c,d$ are formulae, we can show that it does not hold, manufacturing a simple counterexample.

Consider as $d$ the formula: $a \land b \land c$; clearly:

$a,b,c \vDash a \land b \land c$

but $a \nvDash a \land b \land c$, and the same for $b$ and $c$.