Write the negation of the given statement and determine which is true 1. Any eve

Question

Write the negation of the given statement and determine which is true
1. Any even integer equals twice some other integer
2. There is a prime number between every integer greater than 1 and it's double Write the negation of the given statement and determine which is true
1. Any even integer equals twice some other integer
2. There is a prime number between every integer greater than 1 and it's double
1. Any even integer equals twice some other integer
2. There is a prime number between every integer greater than 1 and it's double

Explanation / Answer

Solution:-

1. Any even integer equals twice some other integer,

this given statement is true, as for example, 4 = 2 x 2, 6 = 2 x 3, 1000 = 2 x 500, etc, and thus is true for all.

Negation of this statement - Any odd integer is not equals to twice some other integer.

2. There is a prime number between every integer greater than 1 and it's double.

this given statment is true, as there is always atleast one prime number between n and 2n, if suppose we choose 9 as an integer which is greater than 1, and its double is 18.

There are, three prime numbers in between 9 and 18, which are 11, 13, 17.

Negation of this statement - There is not a prime number between every integer greater than 1 and it's double.

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