Question

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

Answer 1

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