Description Q?1: [4+4 marks] Determine whether the proposition is a tautology. Let be a universa ...

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Description Q?1: [4+4 marks] Determine whether the proposition is a tautology. Let be a universal set and let and be sets. Find i.The sets and . ii.The power set . Q­?2: [2+3+3 marks] Find integers and such that . Find the GCD and LCM for the numbers 2772 and 37800. c)Encrypt the message “I NEED HELP” by translating the letters into numbers, applying the encryption function , and then translating the numbers back into letters. Q­?3: [4×2] Let and be the functions from to . Find . Is onto? Is g one-to-one? Explain you answer. Check whether exists. If it is so, define . Otherwise, provide a reason for not existence of . Check whether exists. If it is so, define . Otherwise, provide a reason for not existence of . Q­?4: [4+4 marks] Of 32 people who save paper or bottles (or both) for recycling, 30 save paper and 14 save bottles. Find the number of people who b)Students need to answer 8 out of 10 questions in biology exam. save both save only paper, and save only bottles. Find the number of the ways a student can choose the 8 questions. In how many ways can a student choose 8 questions if the first three questions are mandatory? In how many ways can a student choose 8 questions if at least 4 of the first 5 questions must be answered? Q­?5: [2+3+3 marks] Consider an experiment of rolling two dice, and assume that each simple event in the sample space is as likely as any other find the probability that: A sum of 7 turns up; A sum of 7 or 11 turns up; A sum is greater than 3 is obtained.