 In a previous video, I wanted a program to ask for a user's gender. I translated this English expression into this Ruby expression, which didn't work. In order to make it work, I had to use AND instead of OR. Well, it turns out that I could have used OR if I had used parentheses to enclose the entire condition. The two expressions that you see here are exactly equivalent, and the reason they're equivalent is because of something called De Morgan's Laws. What De Morgan's Laws say is that if I take A and B two conditions and OR them together and then negate that, that's the same as negating each one individually and combining them with AND. Similarly, if I have conditions A and B and use AND to combine them and then negate the entire expression, that's the same as negating each one individually and combining them with OR. This really does work, and you can see that it works if you draw what's called a truth table. So here's a truth table with conditions A and B and A or B, and here is the opposite, or the negation of A or B. So you can see that true OR true is true, and the opposite of that is false. Now let's fill in the rest of this table by making each one of them negated individually and then combining them with AND. And you can see that when you do that, it turns out that NOT A or B is the same as NOT A AND NOT B. Similarly, if you fill in a truth table for the other De Morgan's Law, you will find that NOT, the combination of A and B, is the same as NOT A OR NOT B, because this column is exactly identical to that column.