Suppose that CFG G defines $T^*$. Does G defines every language $L$ over the alphabet T?

Question

Suppose that CFG G defines $T^*$. Does G defines every language $L$ over the alphabet T ?

Why the answer for this question is false ? G generates every string in the set $T^*$ and if $L$ is a language over T then $L \subseteq T^*$ so G has to generate also every string in $L$.