Consider 4-variable functions $f1, f2, f3, f4$ expressed in sum-of-minterms form as given below. $$f1 = \sum(0, 2, 3, 5, 7, 8, 11, 13)$$ $$f2 = \sum(1, 3, 5, 7, 11, 13, 15)$$ $$f3 = \sum(0, 1, 4, 11)$$ $$f4 = \sum(0, 2, 6, 13)$$ With respect to the circuit given above, which of the following options is/are CORRECT?

To determine the output function $Y$:

1. Output of the AND gate: The AND operation corresponds to the intersection of minterm sets of $f1$ and $f2$:

   $$\text{AND}(f1, f2) = f1 \cdot f2 = \{0, 2, 3, 5, 7, 8, 11, 13\} \cap \{1, 3, 5, 7, 11, 13, 15\} = \{3, 5, 7, 11, 13\}$$

2. Output of the OR gate: The OR operation corresponds to the union of minterm sets of $f3$ and $f4$:

   $$\text{OR}(f3, f4) = f3 + f4 = \{0, 1, 4, 11\} \cup \{0, 2, 6, 13\} = \{0, 1, 2, 4, 6, 11, 13\}$$

3. Output of the XOR gate ($Y$): The XOR operation corresponds to the symmetric difference of the two sets (minterms present in one set but not both):

   $$Y = (f1 \cdot f2) \oplus (f3 + f4)$$

   • Common minterms: $\{11, 13\}$

   • Minterms only in $\text{AND}(f1, f2)$: $\{3, 5, 7\}$

   • Minterms only in $\text{OR}(f3, f4)$: $\{0, 1, 2, 4, 6\}$

   Therefore, in sum-of-minterms form:

   $$Y = \sum(0, 1, 2, 3, 4, 5, 6, 7)$$

4. Product-of-maxterms form: For a 4-variable Boolean function (minterms 0 through 15), the maxterms are the complement of the minterm set:

   $$Y = \prod(8, 9, 10, 11, 12, 13, 14, 15)$$

Hence, options C and D are correct.