Suppose A$1,$A$2,$A$3,...$

is a sequence of formulae. Does the following tautological implication hold?

$\{$A$2$n:n in N$\}$taut$$A$10->$A$15$

a$.$

Yes, if A$15$

is a tautology.

b$.$

Yes, it does.

c$.$

No$,$ it does not hold.

d$.$

Yes, if A$10$

is a tautology.

e$.$

Yes, but only if A$10$

is a contradiction.