1) This is NOT "Calculus". There is a separate "Discrete Mathematics" area.
2) Do you know what a "truth table" is? That's all that's required.
Each of x, y, and z can be "T" (true) or "F" (false) so there are 2^3= 8 possible combinations:
x y z
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F
For the first, \(\displaystyle \overline{\overline{x}\lor y}= \overline{y}\lor z\)
Step through the eight cases one at a time:
x= y= z= T. On the left, \(\displaystyle \overline{x}= \overline{T}= F\). \(\displaystyle \overline{x}\lor y= F\lor T= T.\).
\(\displaystyle \overline{\overline{x}\lor y}= \overline{T}= F\).
On the right, \(\displaystyle \overline{y}= \overline{T}= F\) so \(\displaystyle \overline{y}\lor z= F\lor T= T\)
The equation says "T= T" which is a true statement so the first line is
x y z \(\displaystyle \overline{\overline{x}\lor y}= \overline{y}\lor z\)
T T T T
