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mbcsantin
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Homework Statement
Prove A contained B iff A n B = A
Homework Equations
none
The Attempt at a Solution
I tried to do the questions but I am just not sure if i did it right. id appreciate if you can check my work and let me know what changes i have to make. thanks
the symbol "n" means "intersect"
U for Union
(=>) Assume A contained B
Let x is an element of A, since A n A = A, x is an element of A and x is an element of B
Case 1: x is an element of A: Since A contained B, x is an element of B so
x is an element of A n B
Case 2: x is an element of B: If x is an element of B then
x is an element of (A n B)
Hence x is an element of A n B
This shows A contained A n B
(<=) Assume A n B = A then
A’=A’UA
= A’ U (A n B)
=(A’UA) n (A’U B)
= empty set n A’ U B
= A’ U B
Hence
Universe = A’ U B