What are the steps to show that the propositional function 3" < n! true for all n>8? First show P(7) is true. Then, assume P(k) is true. Finally, show that P(k+1) is true. First show P(8) is true. Then, assume P(k) is true. Finally, show that P(k+1) is true. O First show P(8) and P(k) are true. Then, show that P(k+1) is true. OFirst show P(1) is true. Then, assume P(k) is true. Finally, show that P(k+1) is true. O First show P(1) and P(k) are true. Then, show that P(k+1) is true.

For each of the statements below, indicate if it is true or false. You donot have to provide an explanation.(a) (∀n ∈ Z) (∃m ∈ Z) (n = (m^2) + 5)(b) (∀n ∈ Z) (∃m ∈ Z) (m = (n^2) +5)(c) (∃a ∈ Z) (∀b ∈ Z) (a != b + 10)      ( != not equal to)(d) (∃a ∈ Z) (∀b ∈ Z) (a < b^2)(e) (∀n ∈ Z) (∃m ∈ Z) (∃p ∈ Z) (mp + 3 = n)

10] Javier works each weekend at an animal shelter where he earns $8 an hour. He is saving his earnings to go on a ski trip that costs $190. Number of Hours Javier's Work Record 10 9 8 0965 1 10 - Saturday |- Sunday Let h be the number of hours Javier worked. Select all the true statements. 10 2 Weekends □ Since 8h <190, Javier did not earn enough money to make the trip.

Exerci (1) Create a truth table for each statement. (a) p^(-p) (b) pv (p^r)