Eduprobe
Question:
The set (A∪B∪C)∩(A∩B'∩C')∩C' is equal to?
B∩C'
B'∩C'
None of these
A∩C
Solution:
(A∪B∪C)∩(A∩B'∩C')∩C'=(A∪B∪C)∩(A'∪B∪C)∩C'=[(A∩A')∪(B∪C)]∩C'=(∅∪B∪C)∩C'=(B∪C)∩C'=(B∩C')∪(C∩C')=(B∩C')∪∅=B∩C'.
B∩C'
B'∩C'
None of these
A∩C
(A∪B∪C)∩(A∩B'∩C')∩C'=(A∪B∪C)∩(A'∪B∪C)∩C'=[(A∩A')∪(B∪C)]∩C'=(∅∪B∪C)∩C'=(B∪C)∩C'=(B∩C')∪(C∩C')=(B∩C')∪∅=B∩C'.