Final answer:
The given proposition is (p → ¬q) ∨ (¬p ∧ r). It evaluates to true if either p is false and q is false, or p is false and r is true.
Step-by-step explanation:
The given proposition is (p → ¬q) ∨ (¬p ∧ r). Let's break it down step by step:
- p → ¬q: This statement means 'if p is true, then q is not true'. In other words, if p is true, q must be false.
- ¬p ∧ r: This statement means 'not p is true and r is true'. In other words, p must be false and r must be true.
Now, we have two sub-statements: 'p is false and q is false' or 'p is false and r is true'. These two sub-statements are joined by the 'or' operator, which means at least one of them must be true. Therefore, the overall proposition is true if either p is false and q is false, or p is false and r is true.