12)By giving a counter example, show that the following statement is false. Ifn is an odd integer, then n is prime.

Question

Question

12)By giving a counter example, show that the following statement is false.

Ifn is an odd integer, then n is prime

.

maths

Answer 1

Answer #1

Solution

The given statement is in the form ifp then g' we have to show that this is

false. For this purpose we need to show that if p 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=9is 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

answered by: Vijayan

Answer 2

Similar Homework Help Questions

14)by giving a counter example ,show that the following statements is false .if n is an odd integer ,then n is prime

14)by giving a counter example ,show that the following statements is false .if n is an odd integer ,then n is prime
1 a). Give a counter example to the proposition: Every positive integer which ends in 31...

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 +...
5. Consider the following N-N function f: 4n+1 ifn is odd if n is even. Representing...

5. Consider the following N-N function f: 4n+1 ifn is odd if n is even. Representing numbers in binary: (a) give an implementation level description in English of a Turing machine that computes this f; (b) give the complete transition table of this Turing machine. (4 marks) (6 marks)

Show that if n is a positive integer and a and b are integers relatively prime to 1 such that (On...

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...

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...

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.

The prime factorization of a positive integer n is p^3. Which of the following is true?...

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.
(1 point) If a statement has an example that proves it true, please enter it. If...

(1 point) If a statement has an example that proves it true, please enter it. If instead a statement is able to be disproved, please enter 'F' for false. If you enter an example, please use the one with the smallest possible absolute value. For instance, if 3 and -1 are both counter examples, then the correct answer is -1. 1. 3x E Z(Prime(12.2 +21)) 2. Fx e R \ {0} Vy e R(xy = x) 3. There is a...
Decide whether each statement is true or false and explain your reasoning. Give a counter-example...

Decide whether each statement is true or false and explain your reasoning. Give a counter-example for false statements. The matrices A and B are n x n. a. The equation Ax b must have at least one solution for all b e R". b. IfAx-0 has only the trivial solution, then A is row equivalent to the n x p, identity matrix. c. If A is invertible, then the columns of A-1 are linearly independent. d. If A is invertible,...

Let n be a positive integer. Show that nº + 4n +5 has no prime divisor...

Let n be a positive integer. Show that nº + 4n +5 has no prime divisor p with p 3 mod 4.