.Let A, B, and C be languages over some alphabet Σ. For each of the following statements, answer "yes" if the statement is always true, and "no" if the statement is not always true. If you answer "no," provide a counterexample.

a) A(BC) ⊆ (AB)C

b) A(BC) ⊇ (AB)C

c) A(B ∪ C) ⊆ AB ∪ AC

d) A(B ∪ C) ⊇ AB ∪ AC

e) A(B ∩ C) ⊆ AB ∩ AC

f) A(B ∩ C) ⊇ AB ∩ AC

g) A∗ ∪ B∗ ⊆ (A ∪ B) ∗

h) A∗ ∪ B∗ ⊇ (A ∪ B) ∗

i) A∗B∗ ⊆ (AB) ∗

j) A∗B∗ ⊇ (AB) ∗