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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

SamGibson
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gobears21
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  • Is `¬y` meant to be \$\bar{y}\$? – Andy aka Feb 17 '22 at 09:31
  • @Andyaka they're equivalent notations, yes – Ilya Feb 17 '22 at 10:06
  • @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. – Andy aka Feb 17 '22 at 10:09
  • some people use different notations in different countries. But yeah, it was a weird thing to assume about you lol. – Ilya Feb 17 '22 at 10:10
  • @gobears21 unate in what variable? Why don't you check it according to definition of unate function? – Ilya Feb 17 '22 at 10:11
  • @Andyaka I want to express a NOT with a short bar above a variable, but I don't know how to do that. – gobears21 Feb 18 '22 at 03:27
  • @Ilya the unate in the question refers to function f is constant, monotonically increasing or monotonically decreasing. – gobears21 Feb 18 '22 at 03:28

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