# If two Boolean functions $f_1$ and $f_2$ have same truth table, does that means they have exactly same characteristic? can one f1 numerate to f2?

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

• Is ¬y meant to be $\bar{y}$? Feb 17 at 9:31
• @Andyaka they're equivalent notations, yes
– Ilya
Feb 17 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. Feb 17 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 at 10:10
• @gobears21 unate in what variable? Why don't you check it according to definition of unate function?
– Ilya
Feb 17 at 10:11