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Which of the following expressions is not equivalent to $\bar{x}$?

1. $x \text{ NAND } x$
2. $x \text{ NOR } x$
3. $x \text{ NAND } 1$
4. $x \text{ NOR } 1$

1. $\overline {x x}= \bar x$
2. $\overline {x+x}= \bar x . \bar x =\bar x$
3. $\overline {x .1 }= \bar x + 0= \bar x$
4. $\overline {x +1}= \bar x. 0 = 0$

Here, $x \text{ NOR }1$  will  not be equal to $\bar x.$

Hence, option (D) $x \text{ NOR} \ 1$ .

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(3) is calculation is not correct...1+anything =1 ...
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Updated Thanks!

x OR 1 = 1 and so x NOR 1 = 0.

x NAND x

Lets do it for AND first

x AND x = x (Idempotent property)  Now take negation on both side  ____   __

x.x =  x

x NOR x

Lets do it for OR first

x OR x =x (Idempotent property) Now take negation on both side   _____     ___

x + x   =    x

x NAND 1

Again do it for AND first    x AND 1 = x Take negation on both side   ____    __

x .1 =  x

x NOR 1

Do it for OR first

x OR 1 = 1   Noe negate on both side    ______     __

x + 1   =  1     = 0

NOTE - Line (---------     ----)  are representing negation

D), as X nor 1 will always be 0, irrespective of state of X
x nor x means complement of (x+x) that is x's complement so equal, only d differs as it evaluates to 0

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