Question

Using DeMorgan's law determine which of the following Boolean expressions are equivalent to the Boolean expression shown below. Y =(A+B)D+C AY = (ABDC) BY = (A+B)(D+) CY - (AB+DC D. Y = (AB)+(DC) EY = A +B) + (D+C) F. Y = (AB+D) +

Answer 1

• Below is the detailed explanation of the above problem on DeMorgan's law.
• Correct option is C i.e,
  (AB + D)
  .
• Explanation:

DeMorgan's law: Basically, there are two equations i.e,

1.

A.B=A+B

2.

A+B= AB

So we will use these two in proving the boolean expressions.

• For option A:

Ye (ĀB)() -> (A+B).(D+c) (using ĀB - ATB) (A+B) +(016) (using +B) + A+B (A+B) DTC Ā B. Atb 7

• For option B:

(ATB) (o to 2 N (A-6) (DT) A (using à +B z AB) (using A B ² ATB) + AB+ DC (ATB)ote

• For option C:

Y e CAB + D (+ ) (A+B+ D) T => ((A+BID). T - (B (A + B) DIC (using Ā B . ATB) (using A + B z AB (Using Ā B ² ATB) Z (A+B) DTC

• For option D:

Yz (AB) HDC) (ATB) + (Dro) >> ( using A B z A+B) ( Using A + B z A.B) - (ATB) (oto) 7 (A+BIDIC

• For option E:

Yz (A+B) +5 to = ( (AB) + (DC) (using A + B 2 AB ( B Using A + B e AB) AB, DC Ť (A+B) DAC

• For option F:

Y e CĀŠto) + ł (A + B + D) + (using AB ² ATB) =) ((A+B). D) tí (using At B 2 AB (A+B) D.C. (using ĀTB e AB + (A1BDtc. +

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