# 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
Turingâ€™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.