Question

Fie multimile:A={x|x∈N, x≤4},B={x|x∈N,x<5,x par},C={x|x∈N, 2≤x≤5} a)Aflati:AUB,AUC,BUC,AUBUC ,U este reuniune b) verificați ca AUB=BUA,(AUB)UC=AU(BUC

Answer 1

A = {0,1,2,3,4}     B = { 0,2,4}   C = {2,3,4,5} 
a)  A∪B = {0,1,2,3,4}    A∪C = {0,1,2,3,4,5}    B∪C = { 0,2,,,3,4,5}
A∪B∪C = {0,1,2,3,4,5}
b) A∪B = { 1,2,3,4}   B∪A = { 0,1,2,3,4} ⇒  A∪B = B∪A
(A∪B)∪C = {0,1,2,3,4} ∪ { 2,3,4,5} = {0,1,2,3,4,5}
A∪(B∪C) + {0,1,2,3,4}∪{2,3,4,5} = {0,1,2,3,4,5}