Download OU BA 2017 2nd Year 7066 Logic and Sets Question Paper

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FACULTY OF SCIENCE

B.Sc. III-Semester (CBCS) Examination, December 2017

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Subject: Mathematics

Paper - III

Logic and Sets

Time: 1½ Hour Max.Marks: 40

PART - A (2x5 = 10 Marks)

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[Short Answer Type]

Note: Answer all questions. Each question carries equal marks.

1. a) Show that the statement - (p?q) ? ¬q is a tautology

   OR

   b) Show that statements p?(¬q?r) and p?(q?¬r) are logically not equivalent.
2. a) For any finite set A with |A| = n = 0 then prove that |P(A)| = 2ⁿ

   OR

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   b) Express A - B in terms of U and -.

PART - B (2x15 = 30 Marks)

[Essay Answer Type]

Note: Answer all questions. All questions carry equal marks.

3. a) Let s and t be statements that contain no logical connective other than ? and ?. If s?t then s^d?t^d.

   OR

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   b) Hypothesis: If I join OU then I will get best education. If I get best education then I will get job in USA. If I get job in USA then I will become a millionaire. I joined OU. Conclusion: I will become a millionaire. Give an argument using rules of inference to show that the conclusion follows from the hypothesis.
4. a) Let S be the sample space for an experiment E. For events A, B, C?S Pr(A?B?C) = Pr(A)+Pr(B)+Pr(C)-Pr(AnB) - Pr(AnC) - Pr(BnC) + Pr(AnBnC).

   OR

   b) A man alternatively tosses a coin and throws a die beginning with coin. Find the probability that he will get a head before he gets a 5 or 6 on the die.

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