Thanks for reading.

I'm currently reading Tom Mitchell's Machine Learning (I'm a beginner into ML), and I'm on chapter 4 about perceptrons. I'm really confused about this paragraph:

enter image description here

I understand the AND but I'm still not so sure how OR can be represented.

For example, if the inputs are:

$X_1 = +1$

$X_2 = -1$

In that case, using his logic for OR we would end up with the perceptron actually outputting -1, because:

$1*0.5 + -1*0.5 - .3 = -.3$

The function would give us a negative number. Is he wrong about the OR function? How would a single perceptron act as an OR?

Thank you!

  • 1
    $\begingroup$ I agree with your logic. However, notice that even if the value of -0.3 is mistyped, the construct is still possible. Consider setting w_0=0.3 in order to achieve the desired OR effect. $\endgroup$
    – mapto
    Dec 17, 2018 at 16:43
  • $\begingroup$ @mapto that makes sense, he just messed up the sign. Thank you! On a completely different note, do you happen to know if the book mentioned above is a good book for learning, or have any recommendations? $\endgroup$ Dec 17, 2018 at 17:15
  • 1
    $\begingroup$ I'm sorry, I can't help. Notice, however, that Mitchell's book is more than 10 years old and the field has developed a lot. Unless there is a new updated edition, I'd prefer something more recent. $\endgroup$
    – mapto
    Dec 18, 2018 at 8:05

1 Answer 1


I interpret it as the input takes binary value $0$ (false) and $1$ (true) while the output take $-1$ (false) and $1$ (true).

The map is $$sign\left(\sum_{i=1}^nw_ix_i+w_0\right).$$

If we let $w_i=0.5, i \ge 1$, then we have the mapping rule to be


For the AND operator, if we set $w_0=-0.8$, for it to take positive value both $x_i$ has to be $1$.

For the OR operator, if we set $w_0=-0.3$, we just need one of them to take positive value for it to be true.

  • $\begingroup$ Siong you're awesome. I'm just going to tag you in a comment now every time I ask a question!! $\endgroup$ Jan 23, 2019 at 4:05

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