Prove that (A B)c = Ac Bc (Demorgan’s Law)
a)
1) Let x be an arbitrary element of (A B)c
2) x (A B) (By Definition of Complement)
3) x A but x Ac (Definition of Union And Definition of Complement)
4) x B but x Bc (Definition of Union And Definition of Complement)
5) x Ac, x Bc <-> x Ac Bc
6) But x is an arbitrary element of (AUB)c
7) Thus (A B)c Ac Bc
b) And Conversely
1) Let y be an arbitrary element of Ac Bc
2) y Ac, y Bc (By Definition of intersection)
3) y A, y B (Definition of Complement)
4) y A U B (From b(3))
5) y (A U B)c
6) But y is an arbitrary element of Ac Bc
7) Thus Ac Bc (A B)c
From a7 and b7 we have
(A B)c = Ac Bc
What is wrong in above statements? any help please?
Thank You.
Note: Solution is also atatched in doc file.