Show without using truth tables (you can use the results in the tables on pages 27 and 28) that (p^q) →(p → q). the propositional function p(x) states that "x is the capitol of a state". a

Step-by-step explanation:

Let x represent the number of student tickets that must be sold.

The auditorium can hold at most 125 people. If 73 adult tickets were sold, it means that

73 + x ≤ 125

x ≤ 125 - 73

x ≤ 52

Each student ticket sells for $5 and each adult ticket sells for $7.50.

The drama club must make no less than $790 from ticket sales to cover the show's costs. This means that

5x + 7.5 × 73 ≥ 790

5x + 7.5 × 73 ≥ 790

5x +547.5 ≥ 790

5x ≥ 790 - 547.5

5x ≥ 242.5

x ≥ 242.5/5

x ≥ 48.5

Therefore, the number of tickets that must be sold must not be below 49 and must not be above 52. This is expressed as

(49 ≤ x x ≤ 52)