Sure, here are five solved problems using construction of truth table:
Problem 1: Construct a truth table for the following logical expression: p OR (q AND r)
Solution:
| p | q | r | q AND r | p OR (q AND r) |
| --- | --- | --- | ------- | -------------- |
| T | T | T | T | T |
| T | T | F | F | T |
| T | F | T | F | T |
| T | F | F | F | T |
| F | T | T | T | T |
| F | T | F | F | F |
| F | F | T | F | F |
| F | F | F | F | F |
Problem 2: Construct a truth table for the following logical expression: (p AND q) OR (NOT p)
Solution:
| p | q | NOT p | p AND q | (p AND q) OR (NOT p) |
| --- | --- | ----- | ------- | -------------------- |
| T | T | F | T | T |
| T | F | F | F | F |
| F | T | T | F | T |
| F | F | T | F | T |
Problem 3: Construct a truth table for the following logical expression: (p OR q) AND (NOT p OR r)
Solution:
| p | q | r | NOT p | p OR q | NOT p OR r | (p OR q) AND (NOT p OR r) |
| --- | --- | --- | ----- | ------ | ----------| ----------------------- |
| T | T | T | F | T | T | T |
| T | T | F | F | T | F | F |
| T | F | T | F | T | T | T |
| T | F | F | F | T | F | F |
| F | T | T | T | T | T | T |
| F | T | F | T | T | T | T |
| F | F | T | T | F | T | T |
| F | F | F | T | F | F | F |
Problem 4: Construct a truth table for the following logical expression: (p AND q) AND r
Solution:
| p | q | r | p AND q | (p AND q) AND r |
| --- | --- | --- | ------- | --------------- |
| T | T | T | T | T |
| T | T | F | T | F |
| T | F | T | F | F |
| T | F | F | F | F |
| F | T | T | F | F |
| F | T | F | F | F |
| F | F | T | F | F |
| F | F | F | F | F |
Problem 5: Construct a truth table for the following logical expression: (p OR q) AND NOT(q AND r)
Solution:
| p | q | r | q AND r | p OR q | NOT(q AND r) | (p OR q) AND NOT(q AND r) |
| --- | --- | --- | ------- | ------ | ------------ | ------------------------ |
| T | T | T | T | T | F | F |
| T | T | F | F | T | T | T |
| T | F | T | F | T | T | T |
| T | F | F | F | T | T | T |
| F | T | T | T | T | F | F |
| F | T | F | F | T | T | T |
| F | F | T | F | F | T | F |
| F | F | F | F | F | T | F |
I hope these examples will help you to understand how to construct truth tables for different logical expressions.