EECS 190 Blog

Inference Rules

Rules for \(\wedge\)

[\frac{X,Y}{X\wedge Y}, \frac{X\wedge Y}{X}, \frac{X\wedge Y}{Y}]

Rules for \(\vee\)

[\frac{X}{X\vee Y}, \frac{X\vee Y,X\vdash Z,Y\vdash Z}{Z}]

Rules for \(\Rightarrow\)

[\frac{X\vdash Y}{X\Rightarrow Y}, \frac{X,X\Rightarrow Y}{Y}]

Rules for \(\Leftrightarrow\)

[\frac{X\Rightarrow Y,Y\Rightarrow X}{X\Leftrightarrow Y}, \frac{X\Leftrightarrow Y}{X\Rightarrow Y}, \frac{X\Leftrightarrow Y}{Y\Rightarrow X}]

Note that \(X \Leftrightarrow Y\) and \(X = Y\) are the same thing in propositional logic.

Rules for \(\neg\)

[\frac{X\vdash\mathsf{FALSE}}{\neg X}, \frac{\neg\neg X}{X}]

Rules for \(\mathsf{FALSE}\)

[\frac{X,\neg X}{\mathsf{FALSE}}]

Welcome!

Welcome to my Honors 190 blog. We will be looking at the origins of computing starting in the early 1900s with David Hilbert through Alan Turing’s work in the 1930s. We will learn some logic, the mathematics of computer science, and talk about specification and proof. Finally, we will talk about scholarship and how to survive and thrive at the University.