ক) দেওয়া আছে, A = {x : x মৌলিক সংখ্যা এবং x < 10}
= {2, 3, 5, 7}
খ) দেওয়া আছে, B = {4, 5, 6}
B সেটের উপসেটগুলো হলো: {4, 5, 6}, {4, 5}, {5, 6}, {4, 6}, { 4 }, { 5 }, { 6 }, { }.
'ক' থেকে পাই, A = {2, 3, 5, 7}
দেওয়া আছে, C = {1, 3, 4, 5}
এখন,(A ∪ B) = {2, 3, 5, 7} ∪ {4, 5, 6} = {2, 3, 4, 5, 6, 7}
∴ (A ∪ B) ∩ C = {2, 3, 4, 5, 6, 7} ∩ {1, 3, 4, 5}
= {3, 4, 5} (Ans.)
গ) দেওয়া আছে, U = {1, 2, 3, 4, 5, 6, 7, 8}
B = {4, 5, 6}
C = {1, 3, 4, 5}
'ক' থেকে পাই, A = {2, 3, 5, 7}
এখন, (A ∩ B) = {2, 3, 5, 7} ∩ {4, 5, 6} = { 5 }
A′ = U − A = {1, 2, 3, 4, 5, 6, 7, 8} − {2, 3, 5, 7}
= {1, 4, 6, 8}
B′ = U − B = {1, 2, 3, 4, 5, 6, 7, 8} − {4, 5, 6}
= {1, 2, 3, 7, 8}
বামপক্ষ = (A ∩ B)′ = U − (A ∩ B)
= {1, 2, 3, 4, 5, 6, 7, 8} − {5}
= {1, 2, 3, 4, 6, 7, 8}
ডানপক্ষ = A′ ∪ B′ = {1, 4, 6, 8} ∪ {1, 2, 3, 7, 8}
= {1, 2, 3, 4, 6, 7, 8}
∴ (A ∩ B)′ = A′ ∪ B′ (প্রমাণিত)
