self doubt: Normal Form in DM

Question

If p=1, q=1, r=0 then for given assignment:

a) number of min terms evaluate to 1

b)number of min terms evaluate to 0

c)number of max terms evaluate to 1

d)number of max terms evaluate to 0

Comments

Are you sure this is the complete question?

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yes, its a complete question.

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I think A is asking the same question as D
And C is same as B.

So is A = D = 1
And  B = C = 7?

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please explain your procedure of calculating them.

Answer 1

Minterm = product expression involving all the variable
Maxterm = Sum expression involving all the variable

Number of Minterm/Maxterms possible with n variables = $2^n$

In our case n = 3 which means number of minterms/maxterms = 8

For the given assignment, only way to get a minterm ie a product expression to evaluate as 1 is pq~r       (where ~r denotes r complement)
And the remaining minterms ie 8-1=7 are all evaluated to be 0.

Similarly only maxterm to evaluate as 0 is ~p+~q+r and all remaining 7 are 1.
 

So,

A = D = 1
And  B = C = 7

Comments

for max term it should be ~p+ ~q+ r

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thanks for correcting