1. List the elements of each set. c. Find Ac. a. A : the set of all prime integers less than 30 . d. Find AeB b. B : the set of all bit strings of e. How many subsets of A of length 3 . size 3 are there? c. C : the set of all solutions of f. Find the total number of subthe equation x3x=0. sets of A. 2. For each set in Exercise 1 give ex- 5. Let A and B be sets. Prove that amples of two subsets. a. (AB)c=AcBc 3. Let A be the set of all prime integers less than 20 and B be the set of all odd numbers less than 30 . b. (A1A2An)=A1 a. Find Ac inside the set B. 6. Let A and B be sets. Prove that b. Find AB. a. (AB)c=AcBc c. Find (Ae)c. b. (A1A2An)=A1 d. How many subsets of A of 7. L that size 2 are there? A2cAnc e. How many subsets of A of a. A(BC)=(AB) size 3 are there? (AC) f. Find the total number of sub- b. A(B1B2Bn)= sets of A. (AB1)(AB2) (ABn) 4. Let A be the set of all vowels of the English alphabet and B be the set c. A(BC)=(AB) of the first 10 letters of the alphabet. (AC) a. Find AB. d. A(B1B2Bn)= b. Find AB. (AB1)(AB2) (ABn)