if \$f_1(x,y,z)=\neg xz+x\neg y+\neg xy\neg z+xy\neg z\$ determine if \$f_1\$ is symmetric and whether it is unate.

What I thought is: \$f_1\$=¬xz+x¬y+y¬z, the truth table of \$f_1\$ has the same truth table with the function \$f_b = x\oplus \neg y+x\oplus \neg z\$, if \$f_b\$ is not unate, can I say \$f_1\$ is not unate either?

I asked on Math community, but no one answered it, so, I am trying on this community as well. https://math.stackexchange.com/questions/4382873/if-two-boolean-functions-f-1-and-f-2-have-same-truth-table-does-that-means

  • \$\begingroup\$ Is ¬y meant to be \$\bar{y}\$? \$\endgroup\$
    – Andy aka
    Feb 17 at 9:31
  • \$\begingroup\$ @Andyaka they're equivalent notations, yes \$\endgroup\$
    – Ilya
    Feb 17 at 10:06
  • \$\begingroup\$ @Ilya I was too subtle and you thought I didn't know LOL. You stepped in to help me which is kind but, I wanted the OP to answer and use more conventional notation in his/her question. \$\endgroup\$
    – Andy aka
    Feb 17 at 10:09
  • \$\begingroup\$ some people use different notations in different countries. But yeah, it was a weird thing to assume about you lol. \$\endgroup\$
    – Ilya
    Feb 17 at 10:10
  • \$\begingroup\$ @gobears21 unate in what variable? Why don't you check it according to definition of unate function? \$\endgroup\$
    – Ilya
    Feb 17 at 10:11


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