Boolean Algebra problems
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.
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.
Replies

nareshkumar65391)If z=x*y then z*x is? if * is EXOR operation then answer is y.because when both the symbols are same then it will give 0.
0 EXOR with Y gives y.(EXOR 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. 
SheldonCooper
But how you considered x=0? Is it an assumption? Then what if I take y=0?nareshkumar65391)If z=x*y then z*x is? if * is EXOR operation then answer is y.because when both the symbols are same then it will give 0.
0 EXOR with Y gives y.(EXOR follows associative law so we can change the order of input)
By the way I like the answer of second question.thanks. 
nareshkumar6539I am not assuming x=0. EXOR 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 ]
EXOR 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
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