Question

Prove the following theorems using truth table (a) X + XY = X (b) X + YZ = (X + Y)(X + Z)

Answer 1

I attached you the answer in the picture

Step-by-step explanation:

First, let's see the relationship between the logic gates and truth tables:

The operation of logic gates in relation to one another may be represented and analyzed using a branch of mathematics called Boolean Algebra which, like the common algebra, deals with manipulation of expressions to solve or simplify equations. Expressions used in Boolean Algebra are called, well, Boolean expressions.

AND Gate:

The AND gate is a logic gate that gives an output of '1' only when all of its inputs are '1'. Thus, its output is '0' whenever at least one of its inputs is '0'. Mathematically, A∧B = A · B.

OR Gate:

The OR gate is a logic gate that gives an output of '0' only when all of its inputs are '0'. Thus, its output is '1' whenever at least one of its inputs is '1'. Mathematically, A∨B = A + B.

Having this in mind, we just need to use basic Mathematical Logic operations