Question

I am having a hard time trying to understand how to to create a truth table. It would help if you could also explain what you did too. Thank you in advance.

1) Construct a truth table for the following:

a) f(x,y)= xy+xy’         b) f(x,y,z)= x'yz' + x'yz + xy'z' + xyz' + xyz

Answer 1

Truth table for xy: If x and y both are true then only xy is true.

x	y	xy
0	0	0
0	1	0
1	0	0
1	1	1

Truth table of x + y: If either x or y is true then x + y is true.

x	y	x + y
0	0	0
0	1	1
1	0	1
1	1	1

Truth table of x': If x is not true then x' is true

x	x'
0	1
1	0

a) f(x,y) = xy + xy'

Truth Table:

x	y	y'	xy	xy'	xy + xy’
0	0	1	0	0	0
0	1	0	0	0	0
1	0	1	0	1	1
1	1	0	1	0	1

b) f(x,y,z) = x'yz' + x'yz + xy'z' + xyz' + xyz

Truth Table:

x	y	z	x'	y'	z'	x'yz'	x'yz	xy'z’	xyz'	xyz	f(x,y,z)
0	0	0	1	1	1	0	0	0	0	0	0
0	0	1	1	1	0	0	0	0	0	0	0
0	1	0	1	0	1	1	0	0	0	0	1
0	1	1	1	0	0	0	1	0	0	0	1
1	0	0	0	1	1	0	0	1	0	0	1
1	0	1	0	1	0	0	0	0	0	0	0
1	1	0	0	0	1	0	0	0	1	0	1
1	1	1	0	0	0	0	0	0	0	1	1

If you're still having any doubt then please feel free to ask in the comment section.