a) For each of the following statements, write the converse, inverse and contrapositive statement. Use p = hypothesis and q = conclusion. Also, provide the mathematical notations for the respective statements. (i) If the weather is nice, then I will wash the truck (ii) If n > 5, then, n2 > 25 (iii)~q → (~r∆p)
Question 1
a) For each of the following statements, write the converse, inverse and contrapositive statement. Use p = hypothesis and q = conclusion. Also, provide the mathematical notations for the respective statements.
(i) If the weather is nice, then I will wash the truck
(ii) If n > 5, then, n2 > 25
(iii)~q → (~r∆p)
b) Write each of the following statements in the symbolic form and determine which pairs (if any) are logically equivalent. Ensure that you explain the steps taken and the reason for your decision.
(i) If the goods are unsatisfactory, then your money will be refunded.
(ii) Goods satisfactory or money refunded.
(iii) If your money is not refunded, then the goods are satisfactory.
(iv) If the goods are satisfactory, then your money will not be refunded.
c) Show that (p ∨ q) ∧ (r ∨ ¬ q) → (p ∨ r) is a tautology. Ensure that you explain the steps taken and the reason for your decision.
Step by step
Solved in 3 steps
