Which of the following conjectures is false?
Solution: The false conjecture is:
J. The sum of two odd numbers is odd
Explanation:
F. The product of two even numbers is even.
For example: Let us take two even numbers 4 and 6.
The product of two even numbers is:
[tex]4 \times 6 = 24[/tex]
Therefore, the product is also even number. Hence the conjecture is true.
G. The sum of two even numbers is even.
For example: Let us take two even numbers 4 and 6.
The sum of two even numbers is:
[tex]4+6 = 10[/tex]
Therefore, the sum is also even number. Hence the conjecture is true.
H. The product of two odd numbers is odd.
For example: Let us take two odd numbers 3 and 5.
The product of two odd numbers is:
[tex]3\times5 = 15[/tex]
Therefore, the product is also odd number. Hence the conjecture is true.
J. The sum of two odd numbers is odd.
For example: Let us take two odd numbers 3 and 5.
The sum of two odd numbers is:
[tex]3+5= 8[/tex]
Therefore, the sum is not an odd number. Hence the conjecture is false.
The fourth option is incorrect.
When a number is divisible by 2 then it is called an even number or the number is not divisible by 2 then the number is an odd number.
1. The product of two even numbers is even. This statement is correct.
Example = 2 x 4 = 8
2. The sum of two even numbers is even. This statement is correct.
Example = 2 + 4 = 6
3. The product of two odd numbers is odd. This statement is correct.
Example = 3 x 9 = 27
4. The sum of two odd numbers is odd. This statement is incorrect.
Example = 3 + 9 = 12
Thus, the fourth option is incorrect.
More about the odd and even link is given below.
https://brainly.com/question/924646
