Please type your answers under the questions.
1. Definition: a surjective function
2. Definition: a bijective function
3. Let A=B=R and relation RsAxB, where xA, yB.
Rs={ (x,y) | x2+y2=1 }
Question: is this relation a function? Why?
4. A = { days of the year 2000 }
B = { children who were born in 2000 }
Definition of R1 and R2 relations:
R1AxB, R1 = { (a,b) | for every day from set A, children are assigned from set B, who were born at the same day }
R2BxA, R2 = { (a,b) | for every child from set B his/her birthday is assigned from set A }
Questions: is R1 a function, injective, surjective (and why)? Is R2 a function, injective, surjective (and why)?
5. Use mathematical induction to prove that n<2n for all positive integers n. (If you want you can write your solution to a paper, then please take a picture using your mobile, then please insert the photocopy of your solution here.) 6. A byte to be transferred is 01101110b. Using odd parity, what will be the parity bit and why?