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Homework Statement
Prove that f: S -> T is one-to-one if and only if f(AnB) = f(A) n f(B)
for every pair of subsets A and B of S
Homework Equations
See above
The Attempt at a Solution
Part 1:
Starting with the assumption f(AnB) = f(A) n f(B)
Let f(a) = f(b) [I'm going to try and prove that a=b for one-to-one]
f(a) is an element of f(A)
f(b) is an element of f(B)
f(a) = f (b)
So
f(a) is an element of f(A) n (B)
From assumption
f(a) and f(b) are elements of f(A) n f(B) so also elements of f (AnB)
so a, b are elements of AnB
Can't work out how to show they are equal though..
2. Assume f is one-to-one
So f(a)=f(b) and a=b
If a=b, a is an element of AnB
so f(a) is an element of f(AnB)
Likewise, if f(a)=f(b) then f(a) is an element of f(A) n f(B)
Don't know where to go from here.