Fsc Part 1 Mathematics (Complete Solution)
Q2
Contruct truth tables for the following statements
(i) (p→∼p)∨(p→q)
Solution:
| p | q | ∼p | p→∼p | p→q | (p→∼p)∨(p→q) |
|---|---|---|---|---|---|
| T | T | F | F | T | T |
| T | F | F | F | F | F |
| F | T | T | T | T | T |
| F | F | T | T | T | T |
(ii) (p∧∼p)→q
Solution:
| p | q | ∼p | p∧∼p | (p∧∼p)→q |
|---|---|---|---|---|
| T | T | F | F | T |
| T | F | F | F | T |
| F | T | T | F | T |
| F | F | T | F | T |
(iii) ∼(p→q)↔(p∧∼q)
Solution:
| p | q | ∼q | p→q | ∼(p→q) | p∧∼q | ∼(p→q)→(p∧∼q) | (p∧∼q)→∼(p→q) |
|---|---|---|---|---|---|---|---|
| T | T | F | T | F | F | T | T |
| T | F | T | F | T | T | T | T |
| F | T | F | T | F | F | T | T |
| F | F | T | F | F | F | T | T |