A combinational circuit whose output is equal to $1$ if the input is odd and

greater than two otherwise the output is $0.$ The expression for three inputs

$(x,y,z)$ equals:

$f(x,y,z)=y{z}^{\text{'}}+x^{\text{'}}{z}^{\text{'}}$

$f(x,y,z)=x{z}^{\text{'}}+yz{z}^{\text{'}}$

$f(x,y,z)=xz+yz$

The Boolean function $(F=xz+x^{\text{'}}y+y^{\text{'}}z)$ is implemented with NAND and

inverter gates will be:

$F=((xZ{)}^{\text{'}}+(x^{\text{'}}Y{)}^{\text{'}}+(Y^{\text{'}}Z{)}^{\text{'}}{)}^{\text{'}}$

$F=((xZ{)}^{\text{'}}*(x^{\text{'}}Y{)}^{\text{'}}*(Y^{\text{'}}Z{)}^{\text{'}}{)}^{\text{'}}$

$F=((xZ)*(x^{\text{'}}Y)*(Y^{\text{'}}Z){)}^{\text{'}}$

The complement of $F=W^{\text{'}}{x}^{\text{'}}+Y^{\text{'}}Z+Z^{\text{'}}W$ is $*$

$F^{\text{'}}=W^{\text{'}}+x^{\text{'}}+Y+Z^{\text{'}}+Z+W^{\text{'}}$

$F^{\text{'}}=Wx+Y{Z}^{\text{'}}+Z{W}^{\text{'}}$

$F^{\text{'}}=(W+x)(Y+Z^{\text{'}})(Z+W^{\text{'}})$