A Boolean expression is an expression made out of propositional letters (such as $p, q, r$) and operators $\wedge$, $\vee$ and $\neg$; e.g. $p\wedge \neg (q \vee \neg r)$. An expression is said to be in sum of product form (also called disjunctive normal form) if all $\neg$ occur just before letters and no $\vee$ occurs in scope of $\wedge$; e.g. $(p\wedge \neg q) \vee (\neg p \wedge q)$. The expression is said to be in product of sum form (also called conjunctive normal form) if all negations occur just before letters and no $\wedge$ occurs in the scope of $\vee$; e.g. $(p\vee \neg q) \wedge (\neg p \vee q)$. Which of the following is not correct?
Answer will be (E)
a) True. Every expression can be written in SOP form
b) True. Every expression can be written in POS form
c)True. We can write OR in the form of AND. e.g.(A+B)=not(not(A) . not(B))
d)True.We can write AND in the form of OR e.g. (A .B)=not(not(A) + not(B))
(e)False. We cannot convert NOT gate to any other gate. We cannot also get NAND , NOR such universal gate without NOT gate. So, without NOT gate we cannot get every boolean expression