00:01
We are given equations, and we're asked to find the values, if any, of the boolean variable x that satisfies these equations.
00:12
In part a, the equation is x times 1 equals 0.
00:25
While in a boolean algebra, a variable can only take on the value of 0 or 1.
00:31
So if x takes on a value, the value must be 0 or 1.
00:35
Well, by the definition of a boolean product, if x is equal to 0, then it follows that x times 1 is equal to 0 times 1, which is 0.
00:52
And if x is equal to 1, then x times 1 is equal to 1 times 1, which in a boole in algebra is still 1.
01:07
Okay, therefore, we note that x times 1 equals 0 only when x equals 0.
01:22
In part b, we're given the equation x plus x equals 0.
01:34
Again, this is a bullion algebra, so the variable can only take on the value of 0 or 1, if it takes from the value.
01:42
Now by definition of a boolean sum, if x is equal to 0, then the left side, x plus x is equal to 0 plus 0, which in a boolean algebra, is simply 0.
02:02
And then we have if x is equal to 1, the left side, x plus x becomes 1 plus 1...