Question

With out using truth tables, find the PDNF and PCNF of the following statements (a) )) (P → (P ∧ (Q → P (b) ) (Q → P) ∧ (~ P ∧

Answer 1

Explanation:

Expression mentioned is a Tautology.

((p.q)→r)+((p.q)→r′)=((p′+q′+r)+(p′+q′+r′))=p′+q′+1=1

So PDNF corresponding to it is

(p′.q′.r′)+(p′.q′.r)+(p′.q.r′)+(p′.q.r)+(p.q′.r′)+(p.q′.r)+(p.q.r′)+(p.q.r)

The required normal form is ( if I am not wrong ):-

(p^q^r)v(~p^q^r)v(~p^~q^r)v(p^q^~r)

Once you get the form : (¬p∨¬q∨r)∨(¬p∨¬q∨¬r)

Treat this as (¬p)∨(¬q)∨(r)∨(¬p)∨(¬q)∨(¬r)

And convert the individual literals into minterms.

To convert any variable P to a minterm ,just add : ^(Qv~Q)^(Rv~R) to P

That is :P^(Qv~Q)^(Rv~R)

And then use the distributive laws.