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Hatshy [7]
2 years ago
15

Question is attached as image, please help :>

Computers and Technology
1 answer:
harkovskaia [24]2 years ago
3 0

Answer:

Proved

Explanation:

Given

X = (a.\bar b)+(\bar a.b)

(a + b)\ .  \frac{}{a.b}

Required

Find out why they represent the same

To do this, we simplify either (a + b)\ .  \frac{}{a.b} or X = (a.\bar b)+(\bar a.b)

In this question, I will simplify (a + b)\ .  \frac{}{a.b}

Apply de morgan's law

(a + b)\ .  \frac{}{a.b} = (a + b) . (\bar a + \bar b)

Apply distribution property

(a + b)\ .  \frac{}{a.b} = a.\bar a + a.\bar b + \bar a . b + b . \bar b

To simplify, we apply the following rules:

a.\bar a = 0 --- Inverse law

b.\bar b = 0 --- Inverse law

So, the expression becomes

(a + b)\ .  \frac{}{a.b} = 0 + a.\bar b + \bar a.b + 0

(a + b)\ .  \frac{}{a.b}  = a.\bar b + \bar a.b

Rewrite as:

(a + b)\ .  \frac{}{a.b}  = (a.\bar b)+(\bar a.b)

From the given parameters:

X = (a.\bar b)+(\bar a.b)

This implies that:

(a + b)\ .  \frac{}{a.b} when simplified is X or (a.\bar b)+(\bar a.b)

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