Consider the languages $${L_1}$$, $${L_2}$$ and $${L_3}$$ are given below. $$$\eqalign{ & {L_1} = \left\{ {{0^p}{1^q}\left| {p,q \in N} \right.} \right\} \cr & {L_2} = \left\{ {{0^p}{1^q}\left| {p,q \in N} \right.\,\,and\,\,p = q} \right\}\,\,and \cr & {L_3} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r\, \in N\,\,\,and\,\,\,p = q = r} \right.} \right\}. \cr} $$$

Which of the following statements is not TRUE?

A deterministic finite automation $$(DFA)$$ $$D$$ with alphabet $$\sum { = \left\{ {a,b} \right\}} $$ is given below

Which of the following finite state machines is a valid minimal $$DFA$$ which accepts the same languages as $$D?$$

Consider the languages $$$\eqalign{ & {L_1} = \left\{ {{0^i}{1^j}\,\left| {i \ne j} \right.} \right\},\,{L_2} = \left\{ {{0^i}{1^j}\,\left| {i = j} \right.} \right\}, \cr & {L_3} = \left\{ {{0^i}{1^j}\,\left| {i = 2j + 1} \right.} \right\}, \cr & {L_4} = \left\{ {{0^i}{1^j}\,\left| {i \ne 2j} \right.} \right\}, \cr} $$$

Which of the following statement is false?