Explain thoroughly each question providing examples where necessary; ensure you demonstrate clear understanding of each question;

Discrete mathematics 213; chapter 13;

1. Provide an example of a mathematical proposition explaining your answer.

2. Provide a falsified hypothesis statement making the entire statement to be true.

3. Holding the assumption that the initial value of x=5 explain the Value of x in the equation. X=x+2 where x=1

4. In the following statement, when 3 is even 9 is prime. Explain this statement according to truth value.

5. In a world where dedication is represented by Q, honesty by P and overconfident by R, how best can the statement honesty and dedication is better than overconfident be represented?

6. 101001 is the negation value of which bit? Explain your answer.

7. There are 6 bits string that contains 2 zeroes and 2 ones. Name several examples with reference to the length of 4.

8. The string of a bit having a length of 5 has less than 3 ones and it contains [1,0]. What is the possibility of having more than 10 bit strings and how many strings will be there?

9. What type of complement is this number? 10101100.

10. In a string of length 4 containing [0,1] where two ones are not together, what is the total of strings and what are they?