Boolean Algebra problems

@sheldoncooper-KRWqFp • Oct 8, 2024

Oct 8, 2024

3.5K

1) If z=x*y then z*x is?
Options-
1)x
2)0
3)y
4)1

2) How many functions are possible with 'n' binary variables?

3) How many functions are possible with 2 Boolean variables?

Don't give only answers.I need explanations too.

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nareshkumar6539

@nareshkumar6539-BKuVbx • Nov 21, 2011

1)If z=x*y then z*x is? if * is EX-OR operation then answer is y.because when both the symbols are same then it will give 0.
0 EX-OR with Y gives y.(EX-OR follows associative law so we can change the order of input)
2)with n variables if we construct a truth table then it will contain 2^n entries(rows).In a function that entry may be include or may not be include(we have 2 possibilities)total no.of functions possible with n variables is 2^2^n.
3) if we apply n=2 in the above formula you will get answer 16.
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SheldonCooper

@sheldoncooper-KRWqFp • Nov 22, 2011

nareshkumar6539
1)If z=x*y then z*x is? if * is EX-OR operation then answer is y.because when both the symbols are same then it will give 0.
0 EX-OR with Y gives y.(EX-OR follows associative law so we can change the order of input)
But how you considered x=0? Is it an assumption? Then what if I take y=0?
By the way I like the answer of second question.thanks.
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nareshkumar6539

@nareshkumar6539-BKuVbx • Nov 22, 2011

I am not assuming x=0. EX-OR follows the associate law means even if we change the order of operation result will be never change that i am using there
z=x*y then z*x=?
so i replaced z value in the euation
x*y*x=>(x*x)*y[i apllied associate law ]
EX-OR gives output 1 when both inputs are same ,it gives output 0 when both inputs are same x*x so it will give as output 0
0*y the output of this expression depends on y because
y=0 output is0
y=0 output is1
0