Augustus De Morgan was born in 1806 and died in 1871. He worked in both mathematics and logic, and the following laws are named after him.

Fun fact: De Morgan played the flute! And he was a huge believer in learning for it’s own sake.

## Proposition: De Morgan’s Laws

If and are subsets of a set , then:

## Proof of 1:

### Part 1A

Let , then

- and .
- and

### Part 1B

Now let , then

- and
- and

So, by parts 1A & 1B, the first of De Morgan’s Laws is proved, namely, .

## Proof of 2:

### Part 2A:

Let , then

- and
- and

### Part 2B:

Let , then

- or
- or

So by Parts 2A & 2B, the second of De Morgan’s Laws is proved: .

*Now go lift something heavy,*

Nick Horton