B = {1, 2, 3} ও C = {2, 4, 5} হলে P(B ∩ C) নিচের কোনটির সমান?

প্রশ্ন: B = {1, 2, 3} ও C = {2, 4, 5} হলে P(B ∩ C) নিচের কোনটির সমান?

সমাধান:
B = {1, 2, 3}
C = {2, 4, 5}

(B ∩ C) = {1, 2, 3} ∩ {2, 4, 5}
= {2}

P(B ∩ C) = {{2}, ∅}

P(B) = {1, 2, 3}, {1,2}, {1,3}, {2,3}, {1}, {2}, {3}, ∅}
P(C) = {{2, 4, 5}, {2,4}, {2,5}, {4,5}, {2}, {4}, {5}, ∅}

P(B) ∩ P(C) = {1, 2, 3}, {1,2}, {1,3}, {2,3}, {1}, {2}, {3}, ∅} ∩ {{2, 4, 5}, {2,4}, {2,5}, {4,5}, {2}, {4}, {5}, ∅}
= {{2}, ∅

P(B ∩ C) = P(B) ∩ P(C)