Concept explainers
(a)
To Show: The conjecture is true for the even numbers from 10 to 20.
(a)
Answer to Problem 47PPS
The conjecture is true and the example for it is obtained.
Explanation of Solution
Given:
The Gold Bach’s conjecture states that every number greater than 2 is written as the sum of two primes.
Calculation:
Consider the even numbers is
The sum of the two primes is,
Also,
Thus, the conjecture is true.
(b)
To Find: Thecounterexample if the conjecture is false.
(b)
Answer to Problem 47PPS
The conjecture is false as 3 is the odd number than 2 and 3 is not written as the sum of the two prime.
Explanation of Solution
Given;
All the odd numbers more than the 2 is written as the sum of the two primes.
Calculation:
Since, the number three is not written as the sum of the two prime numbers as the smallest prime number is 2 and
Consider that 3 is the odd number than 2 and 3 is not written as the sum of the two prime. This makes the required counter example for the given statement
This shows that given conjecture is false
Chapter 2 Solutions
Geometry, Student Edition
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