Question #309869
  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.
1
Expert's answer
2022-03-14T07:30:20-0400

Solution (1)


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





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


Solution (2)


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





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




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