When Is L(S ∩ T) Not Equal to L(S) ∩ L(T)?

[TrapMuzik]

Okay, so for the problem before this, I proved that L(S ∩ T ) ⊂ L(S ) ∩ L(T ).

For this problem, I have to give an example where L(S ∩ T ) ̸= L(S ) ∩ L(T ).

So I'm thinking that there are going to be elements in L(S) intersect L(T) that are not in the span of S intersect T. In what sort of case would this happen? I'm not sure what direction to go in.

Thanks!

 

[TrapMuzik]

Figured it out! Never mind