Let S be the set of all strings of 0’s and 1’s of length less than or equal to 4. Define a
map D: S → Z as follows: For all s ∈ S, D(s) = the number of 1’s minus the number of
0’s in s.
Express S in roster notation.
Express the range D(S) in roster notation.
Explain why D is one-to-one or give a counterexample that D is not one-to-one.
Explain why D is onto its range D(S) or give a counterexample that D is not onto
its range.

Question

Let S be the set of all strings of 0’s and 1’s of length less than or equal to 4. Define a
map D: S → Z as follows: For all s ∈ S, D(s) = the number of 1’s minus the number of
0’s in s.
Express S in roster notation.
Express the range D(S) in roster notation.
Explain why D is one-to-one or give a counterexample that D is not one-to-one.
Explain why D is onto its range D(S) or give a counterexample that D is not onto
its range.

anonymous · Answer

@KingGeorge pllzzz heelllppp meeee

kinggeorge · Answer

I've got to go really quickly, but I'll give you some hints.

1. Think binary numbers less than 16 (0-15). You should have 16 elements, list them all.
2. Just take the number of 1's minus number of 0's and list them all.
3. It's not 1-1, just find a counterexample.
4. Also fairly self explanatory.

anonymous · Answer

Thanks kinggggggggggggggggg

kinggeorge · Answer

You're welcome. Did you get it all?

anonymous · Answer

ya i got the 16 elements