Answer
No. Interpreted formally, the statement says, “If carriers do not offer the same lowest fare, then you may not select among them,” or, equivalently, “If you may select among carriers, then they offer the same lowest fare.”
“If carriers do not offer the same lowest fare, then you may not select among them,” is the inverse statement of "If two carriers offer the same lowest fare, then the customer will be free to choose between them." The two statements are not logically equivalent.
Work Step by Step
Recall the definition of only if:
"$\forall x$, r(x) only if s(x)" means "$\forall x$, if ~s(x) then ~r(x)" or equivalently "$\forall x$, if r(x) then s(x).
Recall also the definition of inverse of a statement: A statement of the form: $\forall x \in D$, if P(x) then Q(x),
and as its inverse statement: $\forall x \in D$, if ~P(x) then ~Q(x)."
The inverse is not logically equivalent to the original statement.
