Explain 4 ,5, 11, 12 ,13 ,14, 15 and the new signs ,: 4 A~∩i=1nAi=∪i=1nA~A15 A~∪i=1nAi=∩i=1nA~A1 11 - Maths - Sets

Question

Explain 4 ,5, 11, 12 ,13 ,14, 15 and the new signs ,:

4   A ~ ∩ i = 1 n A i = ∪ i = 1 n A ~ A 1 5   A ~
∪ i = 1 n A i = ∩ i = 1 n A ~ A 1 11     A ~ B =
A ∩ B C

Aarushi Mishra · Accepted Answer

If you write A~B then it means A-B, represents the set of all those elements which are in A but not in B∪i=1nAi=A1∪A2∪A3∪
∪An, i e
 it is the set which is unioun of sets A1, A2,
,An∩i=1nAi=A1∩A2∩A3∩ ∩An, i e
 it is the set which is intersection of sets A1, A2,
,AnA~∪i=1nAi=A~A1∪A2∪A3∪
∪AnUsing the property A-B∪C=A-B∪A-C=A~A1∪A~A2∪A~A3∪
∪A~An=∪i=1nA~AiFor remaining queries, please post them in a new thread

Explain 4 ,5, 11, 12 ,13 ,14, 15 and the new signs ,: 4 . A ~ ∩ i = 1 n A i = ∪ i = 1 n A ~ A 1 5 . A ~ ∪ i = 1 n A i = ∩ i = 1 n A ~ A 1 . 11 . A ~ B = A ∩ B C

Explain 4 ,5, 11, 12 ,13 ,14, 15 and the new signs ,:

$4 . A ~ (\cap_{i = 1}^{n} A_{i}) = \cup_{i = 1}^{n} (A ~ A_{1}) 5 . A ~ (\cup_{i = 1}^{n} A_{i}) = \cap_{i = 1}^{n} (A ~ A_{1}) . 11 . A ~ B = A \cap B^{C}$