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I am trying to figure out if I implemented a 2-1 Mux correctly based on a 3 variable K-map.

my function states F(x,y,z)= Σm(0,1,3,6), and I have created a kmap as follows

  00  01  11 10

0] 1 , 0, 1 , 0

1] 1 , 1 , 0 , 0

Note: the most sig bit is x,and xy are the top inputs and z is the side inputs

from this I found that a 2-1 Mux could be implemented by using z as my selector and ~b=0 and ~a=1, as my inputs to be pushed. Is this correct or have I done this wrong?

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Yes,it's right.You can use z as your selector pin.Here's how finally it's look like

schematic

simulate this circuit – Schematic created using CircuitLab

If you give z=0,the top portion of K-map will be active.That is 00 and 11,for z=0,the output is 1.

    Similarly when z=1,the output F=1 for x=0 (after some simplifications)

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