Prove these left-quotient properties:

1. L1 Cs\L2 iff {8} - L L 2. S\U{L iI) = U{S\L; \i I} 3. a\(L L)= 4. a\L (a\L) L* 5. rev(S\L) - rev (L)/rev(S) - Suppose S C *, , [(a\L)-LU (a\L), if e L, and (a\L) - L2, otherwise.