How to denote “but not” in symbolic logic form?

I'm taking Fundamental Discrete Structure and I want to ask a logical question.

Let p be “Erin reads Berita Harian”, let q be “Erin reads Kosmo”, and let r be “Erin reads Metro”.

Erin reads Berita Harian or Kosmo, but not Metro.

May I know how do I write it in symbolic form? I know that the first one will be "p or q" but how do I include the "but not Metro"?

Thank you.

• "but" is "and." – Randall Feb 20 '18 at 15:03
• Try thinking of "but not" as "and also does not read". – John Hughes Feb 20 '18 at 15:03
• Irrespective of the "tone" , but is gramamticaly classified as a conjunction. – Mauro ALLEGRANZA Feb 20 '18 at 15:11

$(p \cup q ) \cap$~$r$, where $r$ means Erin reads Metro and ~ is used for negation.

But is just a natural language way to say And while simultaneously preparing the reader that the following text might be in contrast to what was stated so far. There is no need to give this meta information in math.

So "A, but not B" just means "A and not B", hence $A\land\neg B$.

"I am rich but not happy"

So, am I rich? Yes. Am I happy? No.

So: $R \land \neg H$

In general, "but" translates into "and"