# 3 variable Kmap into 2-1 Mux

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?