Following Along Async Tutoring [Dface]

[Dface]

@Elliot

OK, so suppose T and F (and 1 and 0) aren’t in your toolkit. You can only use: {and, or, not} and variables. How can you construct T or F? Your answer must work for all possible values the variables could have.

Ok so I cant use expressions like T or F in this activity. How do i construct T or F like i did with other operators? My answer is gonna have “and” or “not” or “or”.

So for T I gotta make an expression that works like it? T makes the desired row true and all other rows false.

For F , the expression will make the desired row false and all other rows false.

For all possible values a variable can have that means:
x,y
1,1
1,0
0,1
0,0

F would make all rows false. All I would need to do is make an expression for one row and negate it.

I actually came up with this:
and(not(x),not(y), y)= F

I read ahead and see maybe the expression T means all rows are true?
I would write: or(x,y,not(x)) = T

I read ahead and I see i was close:

@Eternity

Always false:
(x & !x) | (y & !y)

This is saying that for any set of inputs, the inputs for x and y have to be both be “x and y” and “not x and not y”. That doesn’t work.

Always true:

(x | y) | (!x | !y)

I didnt have to include a second variable. I think it’s just like the expressions T and F. They dont have to include x or y i think

Edit:I included the wrong quote at the end. It was supposed to be this:

@Eternity

So x & !x = always false, or x or !x = always true.