Solve the problem.Show that [p ? (q ? r)] ? [t ? (~p ? (q ? r))](a) by using equivalences.(b) by constructing a truth table.
What will be an ideal response?
| (a) | [p ? (q ? r)] ? [ p ? (~(q ? r)) ? c] | (Reductio ad absurdum) |
| ? [ t ? ~(p ? ~(q ? r)) ] | (Contrapositve) |
| ? [ t ? (~p ?~(~(q ? r))) ] | (De Morgan's law) |
| ? [ t ? (~p ? (q ? r)) ] | (Double negation) |
| (b) | p | q | r | [p ? | (q ? r)] | ? | [t ? | (~p ? | (q ? r))] |
| T | T | T | T | T | T | T | T | T | T |
| T | T | F | T | T | T | T | T | T | T |
| T | F | T | T | T | T | T | T | T | T |
| T | F | F | F | F | T | T | F | F | F |
| F | T | T | T | T | T | T | T | T | T |
| F | T | F | T | T | T | T | T | T | T |
| F | F | T | T | T | T | T | T | T | T |
| F | F | F | T | F | T | T | T | T | F |
| ? | (2) | (1) | (6) | (5) | (4) | (3) |
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Two types of tickets were sold for a concert. Floor seating cost $10.50 a ticket, and balcony seats were $20.20. Use the table to find the total receipts from the sale of both types of tickets. Ticket type Price Number sold Floor$10.501,000Balcony$20.20100
A. $3,070.00 B. $12,520.00 C. $10,702.00 D. $30,700.00 E. none of the above
Write a simplified expression for the following.8 ? 8 ? 8
A. 3 ? 8 B. 81 C. 83 D. 38
Perform the operation. Write the answer as a fraction in lowest terms.
- 
A. 
B. 
C. 
D. 
The 
-coordinate system has been rotated 
degrees from the 
-coordinate system. The coordinates of a point in the
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?
, 
?
A. 
B. 
C. 
D. 
E. 