Consider a Boolean expression given by $F(X, Y, Z) = \Sigma(3, 5, 6, 7)$. Which of the following statements is/are CORRECT?

Given the 3-variable Boolean function:

1. Checking Option A: The minterms are $\{3, 5, 6, 7\}$, so the maxterms (complement minterm set for a 3-variable function from $0$ to $7$) are:

   $$\{0, 1, 2, 4\}$$

   Therefore, in canonical Product of Sums (POS) form:

   $$F(X, Y, Z) = \Pi M(0, 1, 2, 4)$$

   Thus, statement A is correct.

2. Checking Option B: Simplifying $F(X, Y, Z)$ using a Karnaugh map with minterms $m_3(011)$, $m_5(101)$, $m_6(110)$, $m_7(111)$:

   • Grouping $m_3, m_7$: gives $YZ$

   • Grouping $m_5, m_7$: gives $XZ$

   • Grouping $m_6, m_7$: gives $XY$

   Summing the prime implicants gives:

   $$F(X, Y, Z) = XY + YZ + XZ$$

   This is the standard majority function (carry-out of a full adder). Thus, statement B is correct.

3. Checking Options C and D: The minimized expression contains all three variables $X, Y,$ and $Z$, and each literal affects the output value (e.g., $F(0, 1, 1) = 1$ while $F(0, 0, 1) = 0$, so $F$ depends on $Y$). Hence, $F$ is not independent of $Y$ or $X$. Thus, statements C and D are incorrect.

Therefore, the correct options are A and B.