The output Y of following circuit for given inputs is : (1) A•B(A + B) (2) A • B (3) 0 (4) A•B

Question

The output Y of following circuit for given inputs is : 

(1) A•B(A + B) 

(2) A • B 

(3) 0

(4) \(\bar{A} \cdot B\)  

Answer 1

Correct option is : (3) 0 

\(\mathrm{Y}=\overline{\mathrm{A}} \cdot \mathrm{B} \cdot(\mathrm{A}+\overline{\mathrm{B}}) \)

\(=\overline{\mathrm{A}} \cdot \mathrm{B} \cdot \mathrm{A}+\overline{\mathrm{A}} \cdot \mathrm{B} \cdot \overline{\mathrm{B}}\) 

\(=\overline{\mathrm{A}} \cdot \mathrm{A} \cdot \mathrm{B}+\overline{\mathrm{A}} \cdot \mathrm{B} \cdot \overline{\mathrm{B}} \) 

\( =0+0=0\)