Prove, or disprove using a counter example:
Let p,q∈R \ Q \, then p−q is irrational.
I don't understand what the back slash between the R and Q means.
Answer
The ∖ sign means substraction of sets. A∖B={x∈A such that x∉B}.
In your case, R∖Q is the set of irrational numbers.
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