1. The relation R is an equivalence relation on the set of integers. Find the distinct equivalence classes of R. mRn - 61 (m2 -n2 ) 2. Find 31329 mod 589. In problems 3 and 4 use the RSA cipher with public key n=3.11=33 and e=13. In problem 3 encode the message into its numeric equivalent and then encrypt it. In problem 4 decrypt the given cipher text and find the original message. 3. QUIZ 4. 027 009 031 026 5. Suppose that each child born is equally likely to be a boy or girl. In a family with four children find the probability of the following events. (a) At least three children are girls. (b) At least one child is a boy