Question

Let P:n² - n - 4 > 0. Check which P(1), P(2), P(3), P(4), P(5) are true.

Answer 1

Only P(3), P(4), and P(5) are true for the inequality P(n): n² - n - 4 > 0, while P(1) and P(2) are false.

Step-by-step explanation:

The inequality P(n): n² - n - 4 > 0 asks us to evaluate which statements P(1), P(2), P(3), P(4), P(5) are true. To find the values of P(n) for each n, we simply substitute the values into the inequality:

• P(1): 1² - 1 - 4 = 1 - 1 - 4 = -4 which is not greater than 0, so P(1) is false.
• P(2): 2² - 2 - 4 = 4 - 2 - 4 = -2 which is not greater than 0, so P(2) is false.
• P(3): 3² - 3 - 4 = 9 - 3 - 4 = 2 which is greater than 0, so P(3) is true.
• P(4): 4² - 4 - 4 = 16 - 4 - 4 = 8 which is greater than 0, so P(4) is true.
• P(5): 5² - 5 - 4 = 25 - 5 - 4 = 16 which is greater than 0, so P(5) is true.

Therefore, P(3), P(4), and P(5) are true while P(1) and P(2) are false.