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total number of functions possible??

F(x,y,z)=F(x’,y,z’)

plzzz explain properly.

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F(x,y,z)=F(x’,y,z’)  is possible when both XYZ and X'YZ' will be present/absent together in the function.

For example, 000 requires 101(0'00') to be in the function or none should be present in the function. It is analogous to the problem of a  couple attending a party. Hence each pair has 2 choices.

Similarly, you will have the following pairs to choose from-

000 --> 101 (0,5)

001 --> 100 (1,4)

010 --> 111 (2,7)

011 --> 110 (3,6)

Now these 4 pairs can be picked in 2^4 ways. Hence 16 functions are possible that satisfy the given constraint.

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