# math using latex! need to kno

INSTRUCTION 1 – Use Latex to write your assignment. For the state diagram , see the example in the template, or
draw it by hand and insert a photo of it

Please check what i have attached, open the [ [ Template Assignment. pdf ( Its the .tex document in pdf, because i cant attach the .tex file here so i put the .tex code in pdf) ] + [ Assignment Template.pdf ] the original pdf format question ] ,,,,,,,, use overleaf.com! to write the Problem 1 question and answer wants it both in pdf and .tex format and Need to know how to write LATEX
Please use latex to write problem 1 question and answers in .text format i also want pdf

you can use the example assignment template there are two file pdf format and .tex (in pdf form because i cant attach .tex file here)

INSTRUCTION 2- If a problem has more questions, write down your answers in the same order as the order of

Problem 1.

For each of the following languages, give the state diagram of a DFA with the specified
number of states that recognizes the language. The alphabet is Σ = {0, 1}.

1. {w: w contains at least one 0 and one 1}, with 4 states.

2. {w: w has 0 in every odd position}, with 3 states.

Problem 2.

Let A and B be two infinite countable sets. Show that A × B is also an infinite countable sets. You
need to show how to obtain an enumeration of A×B if you have an enumeration A = {f(1), f(2), . . .} and
an enumeration of B = {g(1), g(2), . . . , } (in other words you need to explain how you can list one-by-one
all the pairs in A × B.)

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