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D 12645 (Pages : 3) ത്ത ത്ത

FIRST SEMESTER (CBCSS-UG) DEGREE EXAMINATION
NOVEMBER 2021

Mathematics
MTS 1B 01—BASIC LOGIC AND NUMBER THEORY
(2021 Admissions)
Time : Two Hour and a Half Maximum : 80 Marks
Section A

Answer atleast ten questions.

Each question carries 3 marks.

All questions can be attended.
Overall ceiling 30.

1. Verify that p v p= pand pa p= p.

2. Let P(x)denote the statement “x > 3.” What is the truth value of the quantification 3x P(x), where
the universe of discourse is the set of real numbers ?

3. State the barber paradox presented by Bertrand Russell in 1918.

4. Prove that ifn is a positive integer, then n is odd if and only if 5n + 6 is odd.

5. Prove the following formula for the sum of the terms in a “geometric progression” :

1+ ‏بثربم‎ ப பா ‏سے‎

6. Leta and 6d positive integers such that a|b and b|a, Then prove that ச்‌.
7. Briefly explain Mahavira’s puzzle.

8. Find the number of positive integers < 2076 and divisible by neither 4 nor 5.

9. Prove that every composite number 7 has a prime factor £ | vn |

10. Show that any two consecutive Fibonacci numbers are relatively prime.

Turn over

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