- #1
brad sue
- 281
- 0
Hi, I would like some help for the following problems.
please bear with me with my special notation:
I- intersection
U- union
S- universal set
~- complement
I need to prove that: let be A and B two sets. prove
(A U B) I (A I (~B))=A
what I did is:
(A U B) I (A I (~B))
=[(A I B) U A] I [(A I B) U ~B]/distribution
=A I [(~B U A) I (~B U B)]
=A I [(~B U A) U S)
=A I (~B U A)
=(A I (~B)) U (A I A)
=AUA=A //i'm not sure here (A I (~B)) =A
problem 2
Can we conclude that A=B if A,B,C are sets such that
i) A U C = B U C
ii) A I C = B I C
how can I treat this problem?
Thank you for your help
B
please bear with me with my special notation:
I- intersection
U- union
S- universal set
~- complement
I need to prove that: let be A and B two sets. prove
(A U B) I (A I (~B))=A
what I did is:
(A U B) I (A I (~B))
=[(A I B) U A] I [(A I B) U ~B]/distribution
=A I [(~B U A) I (~B U B)]
=A I [(~B U A) U S)
=A I (~B U A)
=(A I (~B)) U (A I A)
=AUA=A //i'm not sure here (A I (~B)) =A
problem 2
Can we conclude that A=B if A,B,C are sets such that
i) A U C = B U C
ii) A I C = B I C
how can I treat this problem?
Thank you for your help
B