Logic Minimization and Optimization

The following expression is corresponds to $$AB+\bar{A}C+BC=AB+\bar{A}C$$

Following expression represents (M is a maxterm) $$Y=f(A,B)=\prod M(0,1,2,3)$$

Which one of the followings is equivalent to $$\bar{A}\bar{B}+\bar{B}\bar{C}+\bar{C}\bar{A}$$

Simplified form of X is $$ABCD+A\bar{B}CD+\bar{A}BCD+\bar{A}C\bar{B}D$$

The following expression simplifies to $$(\overline{A}+B)+(A+\overline{C})+(\overline{B}+\overline{C})$$

Which expression can not be minimized further?

The following expression is equal to which expression? $$(A+B).(\bar{A}+C).(B+C)$$

Which one of the followings is the dual form of the expression shown below?$$AB+\overline{A}C=(A+C)(\overline{A}+B)$$

The Boolean expression Y(A,B,C) = A + BC is to be realized using 2-input gates of only one type. What is the minimum number of gates required for realization?

Realize the below mentioned expression using two 2-input gates. $$X(P,Q,R)=\prod (0,5)$$

Minimize the following expression $$AD+ABCD+ACD+\overline{A}B+ACD+\overline{A}\overline{B}$$

Minimize the following expression $$(A+B).(A+\overline{B})$$

Expand the following expression $$A\oplus B$$

Find the boolean expression $$F(x1,x2,x3)=\sum (0,1,2,3)+\sum _X(4,5,6,7)$$

Boolean functions can be expressed in SOP and POS form. Such two functions are for the following expression $$Y=(A+\overline{B}C)$$

The boolean expression (A + BC) is reduced form of which of the following

Which of the following statements is not correct?

Minimize the following expression $$\overline{\overline{B}+C}+\overline{\overline{A}+\overline{B}+C}+\overline{A+\overline{B}+\overline{C}}+ABC$$

Find the standard SOP expression for the following boolean expression. $$A\overline{B}+AC+BC$$

Find the complement of the following expression. $$Y=ABC+AB\overline{C}+\overline{A}\overline{B}C+\overline{A}BC$$

The minimum boolean function derived from the K-map is

The minimum expression derived from the K-map is

Minimum expression for the K-map is