Use a table to express the solution for the Boolean function?

Question

F(x,y,z) = xy + z

x y z F(x,y,z)

1 1 1

1 1 0

1 0 1

1 0 0

0 1 1

0 1 0

0 0 1

0 0 0

Answer 1

This could be done in a 2-D table.

Total number of columns = 5
Total number of rows = 3

Top row has all possible values for (x,y)
(first column is blank) then (0,0), (1,0), (0,1), (1,1)
Left column has values of z
first row blank (title row for columns 2 to 5)
second row: z=0
third row: z = 1

Table shows 1 in both rows (2 and 3) of last column ((x,y)=(1,1)) and in the bottom row (z=1); zero elsewhere.

I'll try to do it here:

blank: (0,0):(1,0):(0,1):(1,1)
z = 0 : ...0...:...0...:...0...:...1...
z = 1 : ...1...:...1...:...1...:...1...

F(x,y,z) = xy + z
F = 1 when both x and y = 1 or when z = 1

Answer 2

x y z ... xy + z

1 1 1 ... 1
1 1 0 ... 1
1 0 1 ... 1
1 0 0 ... 0
0 1 1 ... 1
0 1 0 ... 0
0 0 1 ... 1
0 0 0 ... 0

Everywhere z is 1, the function is 1 (OR function)
Everywhere x AND y is 1, the function is 1 (OR of the AND)

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