For questions 4 and 5, use the following order for the rows in your truth tables. P Q T T T F F T F F P Q R T T T T T F T F T T F F F T T F T F F F T F F F 5. (14 marks) For each of the pairs of statement forms below, use the truth table method to determine if (i) is logically equivalent to (ii). Show the truth tables, state your answers, and explain briefly. (a) (i) Q → (P ∨ R) (ii) ¬P → (Q → R) (b) (i) R → (P ∧ ¬Q) (ii) (R → P) ∧ ¬Q
For questions 4 and 5, use the following order for the rows in your truth tables. P Q T T T F F T F F P Q R T T T T T F T F T T F F F T T F T F F F T F F F 5. (14 marks) For each of the pairs of statement forms below, use the truth table method to determine if (i) is logically equivalent to (ii). Show the truth tables, state your answers, and explain briefly. (a) (i) Q → (P ∨ R) (ii) ¬P → (Q → R) (b) (i) R → (P ∧ ¬Q) (ii) (R → P) ∧ ¬Q
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
For questions 4 and 5, use the following order for the rows in your truth tables.
P Q
T T
T F
F T
F F
P Q R
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F
5. (14 marks) For each of the pairs of statement forms below, use the truth table
method to determine if (i) is logically equivalent to (ii). Show the truth tables, state
your answers, and explain briefly.
(a) (i) Q → (P ∨ R) (ii) ¬P → (Q → R)
(b) (i) R → (P ∧ ¬Q) (ii) (R → P) ∧ ¬Q
Expert Solution
Ans 5 (a)(i) Q → (P ∨ R) (ii) ¬P → (Q → R)
| P | Q | R | ¬P | P ∨R | (Q → R) | Q → (P ∨ R) | ¬P → (Q → R) |
| T | T | T | F | T | T | T | T |
| T | T | F | F | T | F | T | T |
| T | F | T | F | T | T | T | T |
| T | F | F | F | T | T | T | T |
| F | T | T | T | T | T | T | T |
| F | T | F | T | F | F | F | F |
| F | F | T | T | T | T | T | T |
| F | F | F | T | F | T | T | T |
By truth table we can easily say that Q → (P ∨ R) and ¬P → (Q → R) is logically equivalent because output is same for both the logic for all input
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