boolean expressions

Question

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

Comments

is the answer 16

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yes how ?

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Generally all 8 sets of i/p's can map to 0 or 1, with 2^8 expressions but in this case o/p for 4 sets such as 000,101 and for the other 3 sets it will be same, which will make it 16.

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can you elaborate a little more i m not getting
u r saying output for 101 111 010 000 will be same as they have given condition
then ?

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see in this question the function f(x',y,z')=f(x,y,z)
when both x' and x are present in function like
case 1:if x'yz' is present then xyz must also be present
case 2:similarly for y' in place of y;
case 3: when x'yz is present then xyz' must be present
case 4: y' instead of y
now for each case either it is present or not present. hence we get 2 combination for each case;
ans =2*2*2*2=16

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oh got it thank you so much

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no problem

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i can't get it could you give more information about it

Answer 1

We have 4 pairs here.

(0,0,0) and (1,0,1)

(0,0,1) and (1,0,0)

(0,1,0) and (1,1,1)

(0,1,1) and (1,1,0)

Here all pairs have 2 choices (mapped to either 0 or 1 ).

4 pairs having 2 choices

So 2^4​=16

Hence 16 is the Answer.

Comments

Can you elaborate it more.

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plz elaborate

 

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why you have taken 0,1,2,3