Final Answer:
The truth table for the statement (p∧q)∨r is as follows:
| p | q | r | (p∧q)∨r |
|---|---|---|---------|
| T | T | T | T |
| T | T | F | T |
| T | F | T | T |
| T | F | F | F |
| F | T | T | T |
| F | T | F | F |
| F | F | T | T |
| F | F | F | F |
Explanation:
The truth table for the statement (p∧q)∨r evaluates the possible truth values of the statement based on all combinations of truth values for the variables p, q, and r. The logical operation used here is the disjunction (∨), which is the "OR" operation. Firstly, the conjunction (∧) operation is performed between p and q, and then the result is combined with r using the disjunction operator.
In the truth table, each row represents a unique combination of truth values for the variables p, q, and r. The (p∧q) part evaluates the conjunction of p and q, and then the ∨r operation combines this result with r using the "OR" logic. The final column (p∧q)∨r shows the resulting truth values for the entire statement based on these combinations.
The statement (p∧q)∨r will be true (T) if either the conjunction of p and q is true (irrespective of r) or if r itself is true, or if both conditions are true. Otherwise, the statement evaluates to false (F).