NIMCET 2022 — Computer PYQ

To find which variable the expression is independent of, we simplify it step-by-step:Step 1: Write the original expression.$$Y=AB+A{B}^{\prime }+A^{\prime }C+AC$$Step 2: Group the terms and apply the Distributive Law.Group the first two terms (containing $A$) and the last two terms (containing $C$):$$Y=A(B+B^{\prime })+C(A^{\prime }+A)$$Step 3: Apply the Complement Law ($X+X^{\prime }=1$).$$Y=A(1)+C(1)$$Step 4: Use the Identity Law ($X\cdot 1=X$).$$Y=A+C$$The simplified expression is $A+C$. In this final form, the variable B is absent.$$\therefore \text{The expression is unaffected by the value of }\mathbf{B}$$$$\therefore \text{Correct Option: }\mathbf{C}$$