Consider three 4-variable functions $f_1$, $f_2$, and $f_3$, which are expressed in sum-of-minterms as $$f_1 = \sum (0, 2, 5, 8, 14), \quad f_2 = \sum (2, 3, 6, 8, 14, 15), \quad f_3 = \sum (2, 7, 11, 14)$$ For the following circuit with one AND gate and one XOR gate, the output function $f$ can be expressed as:

From the given logic diagram:

• The output of the AND gate is $g = f_1 \cdot f_2$.

• The output of the XOR gate is $f = g \oplus f_3 = (f_1 \cdot f_2) \oplus f_3$.

1. Compute $g = f_1 \cdot f_2$: The AND operation on minterm sets corresponds to set intersection:

   $$f_1 = \{0, 2, 5, 8, 14\}$$

   $$f_2 = \{2, 3, 6, 8, 14, 15\}$$

   $$g = f_1 \cap f_2 = \{2, 8, 14\}$$

2. Compute $f = g \oplus f_3$: The XOR operation on minterms corresponds to symmetric difference (minterms present in an odd number of inputs):

   $$f_3 = \{2, 7, 11, 14\}$$

   $$f = g \oplus f_3 = (g \cup f_3) \setminus (g \cap f_3)$$

   $$g \cup f_3 = \{2, 7, 8, 11, 14\}$$

   $$g \cap f_3 = \{2, 14\}$$

   $$f = \{7, 8, 11\} = \sum (7, 8, 11)$$

Thus, option (A) is correct.