

Prove that aw і < 2] and J < 2i} is nonregular using the Myhill-Nerode theorem....
Prove that {a i b j | i ≤ 2j and j ≤ 2i} is nonregular using the Myhill-Nerode theorem. That is, exhibit infinitely many pairwise distinguishable strings.
Prove that {01j I ji} (i.e., j . K = i for some integer k) is nonregular by exhibiting in- finitely many pairwise distinguishable strings
Exercise 7.2.16 Use the dimension theorem to prove Theorem 1.3.1: If A is an m x n matrix with m <n, the system Ax = 0 of m homogeneous equations in n vari- ables always has a nontrivial solution.
Let An = {j EN:j<n} for n = 1,2,.... What are D. and A.
Use the Principle of Mathematical Induction to prove that (2i+3) = n(n + 4) for all n > 1.
Prove that if |A| = |Band [B<|A|, then |A| = |B).
Prove
X, Y, Z, JER. XKY Prove Z <# X AND Y<j, if and only if (x,y) [z,j]
use thevenins theorem
5.62 In the network in Fig. P5.62, find V, using Thévenin's theorem. 12 V 1ke w to 5v.<$ 250 kn oi of Figure P5.62
5. Use Rice's Theorem to prove the undecidablity of the following language. P = {< M > M is a TM and 1011 E L(M)}.
Prove
AB _ BC__ AC aven. DEEF DE Prove: <A><D