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Can you do the verification of question d? The last one

Can you do the verification of question d? The last one-example-1
User Twmb
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6 votes

d)

A u (BnC) = (AuB) n (AuC)

A= 2,4,6,8,10,12,14,16,18,20,22,24

B= 3,6,9,12,15,18,21,24

C= 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24

BnC:


B\cap C=3,6,9,12,15,18,21,24

Au(BnC):


A\cup(B\cap C)=2,3,4,6,8,9,10,12,14,15,16,18,20,21,22,24

Now

(AUB):


(A\cup B)=2,3,4,6,8,9,10,12,14,15,16,18,20,21,22,24

(AUC):


A\cup C=1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24

(AUB) n (AUC):


(A\cup B)\cap(A\cup C)=2,3,4,6,8,9,10,12,14,15,16,18,20,21,22,24

Since


2,3,4,6,8,9,10,12,14,15,16,18,20,21,22,24=2,3,4,6,8,9,10,12,14,15,16,18,20,21,22,24

the statement is correct

User Denis Savenko
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