Question

The Boolean function F(x,y)=x′y+xy′+(x′+y′)(xy) can be simplified to:

A. x′y′
B. xy
C. x xor y
D. 1

Answer 1

The boolean function F(x,y)=x'y+xy'+(x'+y')(xy) simplifies to C. x XOR y, by applying boolean algebra rules such as the distributive law and understanding the definition of the XOR operation.

Step-by-step explanation:

The boolean function F(x,y)=x'y+xy'+(x'+y')(xy) can be simplified by applying boolean algebra rules. Let's examine the expression step by step:

• Notice that x'y+xy' is the definition of the exclusive OR (XOR) operation, so it simplifies to x ⊕ y.
• The term (x'+y')(xy) can be simplified by using the distributive law. However, you will notice that each product results in a contradiction (like x × x' which is always 0), so this term simplifies to 0.
• Combining the above, we get x ⊕ y + 0, which simplifies to just x ⊕ y.

Therefore, the function simplifies to C. x ⊕ y, which is the exclusive OR of x and y.