331 views
0 votes
0 votes
The maximum number of boolean expressions that can be formed for the function f(x,y,z) satisfying the relation  f(x',y,z')=f(x,y,z) is _____________

1 Answer

0 votes
0 votes

" f(x',y,z')=f(x,y,z) " It says for the function value of x',y,z' and x,y,z will be same.
suppose x',y,z' = (1,0,1) then x,y,z = (0,0,0) i,e function value at f(1,0,1) = f(0,0,0) = either 0 or 1.. Lets make all such pairs
 

x y z f
0
1
0
0
0
1
2 possible value i.e either 0 or 1
0
1
0
0
1
0
2 possible value i.e either 0 or 1
0
1
1
1
0
1
2 possible value i.e either 0 or 1
0
1
1
1
1
0
2 possible value i.e either 0 or 1

so maximum number of boolean expression that can be form = 2 x 2 x 2 x 2 = 16

Related questions

4 votes
4 votes
3 answers
1
val_pro20 asked May 15, 2019
1,218 views
What is the time complexity for checking whether an assignment of truth values to variables $x_1,\dots ,x_n$ satisfies a given formula $f(x_1\dots,x_n)$?$O(2^n)$$O(g(n))$...
2 votes
2 votes
1 answer
2
val_pro20 asked May 11, 2019
2,606 views
$(a) A = 101010$ and $B = 011101$ are $1’s$ complement numbers. Perform the following operations and indicate whether overflow occurs.$(i) A + B$$(ii) A − B$$(b)$ Rep...
4 votes
4 votes
4 answers
3
vupadhayayx86 asked May 2, 2019
1,354 views
Simplify the following expressionAB’C + A’BC + A’B’CSolution given is A’C + B’C can someone show me how?