Question

Question 3: Answer the following short question   

Questions 3(a): A milk producing factory has four sensors,

First sensor (A) checks the color of milk and if the color is good it turns ON.

Second sensor (B) checks if the label (sticker) of company is correctly pasted and turns ON.

Third sensor (C) checks if the cap of bottle is properly closed and turns ON.

Fourth sensor (D) checks if the weight of the bottle is correct and turns ON if it is correct.

The bottle is shipped when any three of the four sensors are turned ON.

1. Apply your knowledge of Boolean algebra to prove the following expressions. Demonstrate that LHS is equal to the RHS. NOTE: Please show all the steps.                                    [3 Marks]

     

w’ + w (w’B + B’K)’ = w’ + w (B + K’)

pls answer q3 part d

Answer 1

To prove: w’ + w (w’B + B’K)’ = w’ + w (B + K’)

LHS = w’ + w (w’B + B’K)’

LHS = w’ + w((w'B)'(B'K)')    Using De Morgan's Law

LHS = w’ + w((w+B')(B+K'))    Using De Morgan's Law

LHS = w’ + w((wB+wK'+B'B+B'K'))

LHS = w’ + wwB+wwK'+wB'K'    BB'=0

LHS = w’ + wB+wK'+wB'K' ww=w

LHS = w’ + wB+wK'(1+k')

LHS = w’ + wB+wK'

LHS = w’ + w(B+K')

LHS = RHS

Hence proved.