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## 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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