Explore BrainMass
Share

Explore BrainMass

    Discrete Math : 'Onto' Functions

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    To figure how many 'one-to-one' functions' there are from a set with 3 elements to a set with 4 elements --would be-- 4!/(4-3)! or 24.

    How do you figure out how many 'onto' functions there are from a set with 4 elements to a set with 3 elements?

    Please give solution and detailed explanation.

    Thank you.

    © BrainMass Inc. brainmass.com October 9, 2019, 8:45 pm ad1c9bdddf
    https://brainmass.com/math/discrete-math/discrete-math-onto-functions-161552

    Solution Preview

    Suppose I have two sets X={a,b,c} and Y={1,2,3,4}. I can define a function f from X to Y.
    If f is one-to-one, since |X|=3, then |f(X)|=3. We know f(X) is a subset of Y, and |Y|=4, then we need to find 3 elements out of 4 in Y to make the image of f. There are C(4,3)=4! / 3!(4-3)!. Now after I select 3 ...

    Solution Summary

    'Onto' Functions are investigated.

    $2.19