Explanation
To find the Boolean expression from a truth table, we use the Sum-of-Products (SOP) form. In SOP form, we focus on the rows where the output function f is equal to 1.
1. Identify rows where the output f=1:
Looking closely at the given truth table, the function output f is 1 in exactly three rows:
Row 3: x=0, y=1, z=0
Row 6: x=1, y=0, z=1
Row 8: x=1, y=1, z=1
2. Write the Minterm for each row:
In minterm generation:
If an input variable is 0, it is represented with a prime or complement (e.g., x′).
If an input variable is 1, it is represented in its normal form (e.g., x).
Let's derive the product term (minterm) for each identified row:
For x=0,y=1,z=0→Minterm=x′yz′
For x=1,y=0,z=1→Minterm=xy′z
For x=1,y=1,z=1→Minterm=xyz
3. Sum the Minterms to get the final SOP Expression:
By combining all the individual product terms with a logical OR (+) operation, we get:
F=x′yz′+xy′z+xyz
This directly matches option C.
