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MT 131 AOU Discrete Mathematics Integers & Encryption Function Worksheet

MT 131 AOU Discrete Mathematics Integers & Encryption Function Worksheet

Question Description

Q­−2: [2+3+3 marks]

  • Find integers and such that .
  • Find the GCD and LCM for the numbers 2772 and 37800.
  • 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
  • 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


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