MTH202 Quiz 3 Updated Aug 2022 by Attiq Kundi

MTH-202 Quiz-3 BY Attiq Kundi · “Knowledge For Us” · For More Solutions · (Updated at 17-08-2022) · Subcribe

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Attiq’s Group

1. In the proof by contradiction, we lead the assumption to

Answer: absurdity

2. The predicate describing the initial state is called

Answer: pre-condition of the algorithm

3. An integer n is prime number, if and only if for all positive integers r and s, if n= rs then

Answer: r = 1 or s = 1.

Q4. If ‘f’ is a perfect square, then which of the following is the correct representation of ‘r’?

Answer: r = k^2 for some integer k

Q5. Which of the following is not a rational number?

Answer: √7

6. To prove by mathematical induction for 1+2+3+...+n= (n) (n+1)/2 for all positive integers, the basis step is

Answer: 𝒏 ≥ 𝟑

10. The sum of (6-7√2) and (6+ 7√2) is

Answer: 12

11. The sum of two integers is not an even integer when
12. If n is an add integer then ‘3n+2’ is

Answer: odd

13. The sum of any rational number and any irrational number is irrational.

Answer: true

14. A proof by is based on the logical equivalence between a statement and its contrapositive.

Answer: contrapositive

15. For every prime number n, n+2 is prime. Which of the following prime number disproves the above statement.

Answer: n=7

Q16. In basis property the first iteration of the loop is solved for?

Answer: I (0).

17. For all integers n>0 1+2+2^2+ +2^n=

Answer: 2^ (n-1)

18. In division algorithm ‘r’ stands for

Answer: remainder.

19. If n is any positive integer then the sequence 3+6+9+ ---- +3n =

Answer: 3n(n+1)

20. For all positive real numbers a and b, if a<b, then

Answer: a^2 < b^2

Q21. The last step of describing algorithms formally is?

Answer: An end statement

22. If ‘n’ is an odd integer then n^3+n is

Answer: even

23. Proof by uses the equivalence p→q = -q→ �.

Answer: Contraposition

24. The product of an even and odd integer is

Answer: even

25. In the Direct Proof, we show that if the statement p is true, then the statement q is

Answer: True

26. (-1)^n = 1 for n = (^ stands for power)

Answer: 4

Q27. Which of the following is true for n = 1?

Answer: 2^ (2n) – 1 by 3

28. Proof by uses the equivalence p→q =(p⋀ −q)→ �.

Answer: Contradiction

29. Proof by contradiction is a/an method of proof.

Answer: Indirect.