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Question

Given n(A)=285, n(B)=195, n(U)=500, $$n(A \cup B)=410$$, find $$n(A' \cup B')$$.


Solution

$$n(A\cup B)=n(A)+n(B)-n(A\cap B)$$
$$\Rightarrow n(A\cap B)$$$$=285+195-410\\=70$$

Similarly 
$$n(A^\prime \cup B^\prime)$$$$=n(A^\prime)+n(B^\prime)-n(A^\prime \cup B^\prime)$$
                   $$=n(U)-n(A)+n(U)-n(B)-n(U$$ \ $$(A\cup B)$$
                   $$=500-285+500-195-(500-410)\\=430$$

Mathematics

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