Answer to Question #309869 in Discrete Mathematics for Saphira

Question

1. Show that ¬p → (q + r) and q→ (p V r) are logically equivalent.
2. show, by the use of the truth table (truth matrix), that the (p v q)v[(p¬)ʌ(q)] is a contradiction.

Answer 1

Solution (1)

The truth table for both the statements $¬p → (q → r)$ and $q→ (p ∨ r)$ is shown below

From the above truth tables, we can see that the two statements $¬p → (q → r)$ and $q→ (p ∨ r)$ are logically equivalent.

Solution (2)

For the statement, $(p ∨ q) ∧ ((¬p) ∧ (¬q))$ , the truth table is shown below.

From the last column, it is clear that the statement, $(p ∨ q) ∧ ((¬p) ∧ (¬q))$ is a contradiction.