Final answer:
Upon evaluating the conditions for sets A and B, we find that the true statement is '9 is in set A, and 9 is in set B', as 9 satisfies the conditions for both sets A (x > 8) and B (x > 5).
Step-by-step explanation:
The question asks to find which set of statements is true based on the definitions of set A as x + 2 > 10 and set B as 2x > 10. We need to determine which number satisfies both conditions, being in set A and set B.
To determine if a number is in set A, we can solve the inequality x + 2 > 10 which simplifies to x > 8. Therefore, any number greater than 8 belongs to set A.
To determine if a number is in set B, we solve the inequality 2x > 10 which simplifies to x > 5. Therefore, any number greater than 5 belongs to set B.
Now we need to find a number greater than both 8 and 5, which is common to both sets A and B. By checking the options given, we find that only 6 is not greater than 8 and does not satisfy the condition for set A, while all numbers greater than 5 satisfy set B. Thus, the pair 5 is in set A, and 5 is in set B is not true because 5 does not satisfy x > 8. The pair 6 is in set A, and 6 is in set B is not true because 6 does not satisfy x > 8. The pair 8 is in set A, and 8 is in set B is not true because 8 does not satisfy x > 8. The correct pair is 9 is in set A, and 9 is in set B because 9 satisfies both conditions x > 8 and x > 5.