Math 125 Final Exam
INSTRUCTIONS:
• Answer questions clearly and fully. Marks will be deducted for incomplete and poorly
presented solutions.
• Do not start the exam until instructed to do so.
• The total time for t
...
Math 125 Final Exam
INSTRUCTIONS:
• Answer questions clearly and fully. Marks will be deducted for incomplete and poorly
presented solutions.
• Do not start the exam until instructed to do so.
• The total time for the midterm is 120 minutes for writing and 10 minutes for
submission.
• Upload your final document to link created under Assignment area named as Final
exam.
• I will let you know when there are 5 minutes left. If you continue to write after I instruct
you to laydown your pen or pencil, you will lose marks.
• If you wish, provide any comments about the course/instructor/evaluation
materials/doodles on the last page of the exam.
1
Math 125
Instructor: Mandev Singh
Total marks /36
Section A
Each question carries 3 marks. All questions are compulsory
1. a. Write the converse, inverse, and contrapositive of “If Al is Tom’s cousin, then Jim is
Tom’s grandfather.”
b. Is the following argument valid or invalid? Justify your answer.
All real numbers have nonnegative squares.
The number i has a negative square.
Therefore, the number i is not a real number.
2. Write the 8-bit two’s complement for 62 + (-18).
3. Use the extended Euclidean algorithm to find the G.C.D of the 6664 and 765 and express
it as a linear combination of two numbers.
4. A sequence a0, a1, a2, . . . satisfies the recurrence relation ak=4 ak-1-3 ak-2 with
initial conditions a0 = 1 and a1 = 2. Find an explicit formula for the sequence.
5. A sequence is denoted recursively as follow
a
0=2∧ak=4 ak -1+1 for all k ≥1 . It is proposed that an explicit formula for the
sequence is an=7. 4n-1
3
Use the mathematical induction to check whether this proposed formula is correct.
6. Construct a algebraic proof that for all sets A, B and C, Explain and give detail of each
law by writing at each step.
( AUB )-C=( A-C )U (B-C)
Section
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