14)by giving a counter example ,show that the following statements is false .if n is an odd integer ,then n is prime
The given statement is in the form if p then q" we have to show that this is
false. For this purpose we need to show that ifp then ~q. To show this we look for an
odd integer n which is not a prime number. 9 is one such number. So n =9 is a counter
example. Thus, we conclude that the given statement is false.
In the above, we have discussed some techniques for checking whether a statement
is true or not.
14)by giving a counter example ,show that the following statements is false .if n is an odd integer ,then n is prime
12)By giving a counter example, show that the following statement is false.Ifn is an odd integer, then n is prime.
1 a). Give a counter example to the proposition: Every positive integer which ends in 31 is a prime. b). Give a proof by cases that min{s, t} + max{s, t} = s + t for any real numbers s and t. Hint: One of the cases you might use is s ≤ t or s < t. Depending on your choice, what would be the other case(s)? c). Give an indirect proof that if 2n 3 + 3n +...
Show that if n is a positive integer and a and b are integers relatively prime to 1 such that (On(a), On(b))1, then Show that if n is a positive integer and a and b are integers relatively prime to 1 such that (On(a), On(b))1, then
Let T be an acute triangle. The area of T is denoted by A. If the length of each side of T' is an odd prime number 3 show that A2 is an integer. 16 Let T be an acute triangle. The area of T is denoted by A. If the length of each side of T' is an odd prime number 3 show that A2 is an integer. 16
Problem 7. Let M = 2" – 1, where n is an odd prime. Let p be any prime factor of M. Prove that p=n·2j + 1 for some positive integer j.
5. (a). Find a counterexample to show that 'n € 7,92 +9n+61 is prime" is false. (b). Determine the truth value of "Vee R+ In € Z and justify your answer 6. Write the negation of the following statements (without using in the final answer) (a). Vn € Z, p € P. ** <p<(n+1) (b). Vce R+ 3K € Zt. Vn € Z,n > K-1 Sc.
The prime factorization of a positive integer n is p^3. Which of the following is true? Explain and show your answers. I. n cannot be even II. n has only one positive prime factor. III, n has exactly three distinct factors.
Let n be a positive integer. Show that nº + 4n +5 has no prime divisor p with p 3 mod 4.
Let p be an odd prime and a an integer with p not dividing a. Show that a(p-1)/2 is congruent to 1 mod p if and only if a is a square modulo p and -1 otherwise. (hint: think generators)
A Prime Number is an integer which is greater than one, and whose only factors are 1 and itself. Numbers that have more than two factors are composite numbers. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. The number 1 is not a prime number. Write a well-documented, Python program - the main program, that accepts both a lower and upper integer from user entries. Construct a function, isPrime(n), that takes...