Solutions - 5010-03

(a)

S_{1} = {a b c d \in {G, B}^{4} : c = B}

(b)

S_{2} = {a b c d \in {G, B}^{4} : a = b = c = d}

(c)

S_{3} = {a b c d \in {G, B}^{4} : a b c d \neq G G G G}

(d)

S_{4} = {a_{1} a_{2} a_{3} a_{4} \in {G, B}^{4} : a_{i} \neq a_{i + 1}, i \in {1, 2, 3}}

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