Respuesta :
SOLUTION
A non-negative integer is either positive or zero. It's the union of the natural numbers and the number zero.
A prime number is a number with only two factors, which are 1 and the number itself
Let consider the number
[tex]2[/tex]1) It satisfies the first statement
M is prime
2 is prime
2) M+3 is prime
since
[tex]\begin{gathered} m=2 \\ 2+3=5\text{ } \\ 5\text{ is prime } \end{gathered}[/tex]Hence
The second statement is satisfied
The third statement says
[tex]\begin{gathered} 1<\sqrt[]{m}<8 \\ \text{which is } \\ 1<\sqrt[]{2}<8 \end{gathered}[/tex][tex]\begin{gathered} \text{ since } \\ \sqrt[]{2}=1.414\ldots \\ \text{the third statement is satisfied } \end{gathered}[/tex]Hence the third statement is satisfied
M=2
Since exactly 3 of the 4 statements is satisfied
From the second condition,
[tex]M+3\text{ is prime }[/tex]All prime numbers except 2 are odd numbers
Also,
The sum of two odds is even
[tex]\text{let n be the prime numbers satisfying all the given conditions above }[/tex]from the second condition,
M+3 is prime
[tex]\begin{gathered} n+3\text{ is even } \\ \text{which contradicts the second conditions } \end{gathered}[/tex]Hence
There is no other prime number that satisfies exactly three of the four conditions above
Therefore,
The number of non-negative integers that satisfy exactly three of the four conditions is 1
There is only one non-negative integer M which is 2 that satisfy the condition 1,2,3 above
