Consider the following languages:

L₁ = {aⁿ waⁿ | w $$\in$$ {a, b}*}

L₂ = {wxw^R | w, x $$\in$$ {a, b}*, | w | , | x | > 0}

Note that w^R is the reversal of the string w. Which of the following is/are TRUE?

Consider the following languages:

$$\eqalign{ & {L_1} = \{ ww|w \in \{ a,b\} *\} \cr & {L_2} = \{ {a^n}{b^n}{c^m}|m,\,n \ge 0\} \cr & {L_3} = \{ {a^m}{b^n}{c^n}|m,\,n \ge 0\} \cr} $$

Which of the following statements is/are FALSE?

The ___________ is too high for it to be considered __________.

A function y(x) is defined in the interval [0, 1] on the x-axis as

$$y(x) = \left\{ \matrix{ 2\,if\,0 \le x < {1 \over 3} \hfill \cr 3\,if\,{1 \over 3} \le x < {3 \over 4} \hfill \cr 1\,if\,{3 \over 4} \le x < 1 \hfill \cr} \right.$$

Which one of the following is the area under the curve for the interval [0, 1] on the x-axis?