Question

Is the following compound proposition satisfiable? Justify your answer. (p∨q)∧(m∧¬q)∧(¬q→¬p)

Answer 1

The compound proposition (p∨q)∧(m∧¬q)∧(¬q→¬p) is satisfiable because each component proposition within it can be satisfied.

Step-by-step explanation:

The compound proposition (p∨q)∧(m∧¬q)∧(¬q→¬p) is satisfiable. To justify this, we can consider the truth values of each component proposition. Let's break it down:

1. p∨q - This proposition is satisfiable because at least one of p or q must be true for the entire compound proposition to be true.
2. m∧¬q - This proposition is also satisfiable, as both m and ¬q can be true at the same time.
3. ¬q→¬p - This proposition is also satisfiable. When q is false (¬q), ¬q→¬p becomes true, regardless of the truth value of p. So the entire compound proposition is satisfiable.

Therefore, the compound proposition (p∨q)∧(m∧¬q)∧(¬q→¬p) is indeed satisfiable.