Question

simplified function for the switching function F(x,y) = x+xy is:
a) X
b) Y
c) X+Y
d) XY​

Answer 1

The simplified function for the switching function F(x,y) = x + xy is x

Correct question : The simplified function for the switching function F(x,y) = x + xy is

a) x b) y c) x + y d) xy

Given :

The switching function F(x,y) = x + xy

To find :

The simplified function for the switching function F(x,y) = x + xy is

a) x

b) y

c) x + y

d) xy

Solution :

Step 1 of 2 :

Write down the given switching function

Here the given switching function is

F(x,y) = x + xy

Step 2 of 2 :

Find simplified function for the switching function

We know that if x is a switching variable, then

x + 1 = 1

x . 1 = x

Thus we get

$\displaystyle \sf{ F(x,y) }$

$\displaystyle \sf{ = x + xy }\: \: \: \bigg[ \: \because \: x.1 = x\bigg]$

$\displaystyle \sf{ = x .1+ xy }$

$\displaystyle \sf{ = x .(1 + y )} \: \bigg[By \: Distributive \: Property \bigg]$

$\displaystyle \sf{ = x .1 }\: \: \: \bigg[ \: \because \:1 + y = 1 \bigg]$

$\displaystyle \sf{ = x\: \: \: \bigg[ \: \because \: x.1 = x\bigg] }$

So the simplified function for the switching function F(x,y) = x + xy is x

Hence the correct option is a) x

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