We have shown how to use truth tables to determine if two formulas are truth-functionally equivalent. If two formulas F and G are truth-functionally equivalent we introduce another symbol ↔, aptly called the biconditional. Here is the truth table for the biconditional. p q (p ↔ q) 1 1 1 1 0 0 0 1 0 0 0 1 Now we shall say that F and G are truth-functionally equivalent if (F ↔ G) is a tautology. There are other properties of two formulas that we are usually interested in besides truth-functional equivalence. One of these properties is when two formulas are mutually exclusive. We say two formulas F and G are mutually exclusive if (F ∧ G) is contradictory (unsatisfiable). Now using truth tables determine whether the following formulas are truth-functionally equivalent or mutually exclusive. (a) p and ¬p (b) p and ¬¬p (c) ¬(p ∧ ¬q) and (p → q) (d) (¬p ∨ q) and (p → q) (e) ¬(¬p ∨ ¬q) and (p ∧ q) (f) ¬(¬p ∧ ¬q) and (p ∨ q)
We have shown how to use truth tables to determine if two formulas are truth-functionally equivalent. If two formulas F and G are truth-functionally equivalent we introduce another symbol ↔, aptly called the biconditional. Here is the truth table for the biconditional. p q (p ↔ q) 1 1 1 1 0 0 0 1 0 0 0 1 Now we shall say that F and G are truth-functionally equivalent if (F ↔ G) is a tautology. There are other properties of two formulas that we are usually interested in besides truth-functional equivalence. One of these properties is when two formulas are mutually exclusive. We say two formulas F and G are mutually exclusive if (F ∧ G) is contradictory (unsatisfiable). Now using truth tables determine whether the following formulas are truth-functionally equivalent or mutually exclusive. (a) p and ¬p (b) p and ¬¬p (c) ¬(p ∧ ¬q) and (p → q) (d) (¬p ∨ q) and (p → q) (e) ¬(¬p ∨ ¬q) and (p ∧ q) (f) ¬(¬p ∧ ¬q) and (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
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We have shown how to use truth tables to determine if two formulas are truth-functionally equivalent.
If two formulas F and G are truth-functionally equivalent we introduce another symbol ↔, aptly called the
biconditional. Here is the truth table for the biconditional.
p q (p ↔ q)
1 1 1
1 0 0
0 1 0
0 0 1
Now we shall say that F and G are truth-functionally equivalent if (F ↔ G) is a tautology.
There are other properties of two formulas that we are usually interested in besides truth-functional
equivalence. One of these properties is when two formulas are mutually exclusive. We say two formulas F
and G are mutually exclusive if (F ∧ G) is contradictory (unsatisfiable).
Now using truth tables determine whether the following formulas are truth-functionally equivalent or mutually
exclusive.
(a) p and ¬p
(b) p and ¬¬p
(c) ¬(p ∧ ¬q) and (p → q)
(d) (¬p ∨ q) and (p → q)
If two formulas F and G are truth-functionally equivalent we introduce another symbol ↔, aptly called the
biconditional. Here is the truth table for the biconditional.
p q (p ↔ q)
1 1 1
1 0 0
0 1 0
0 0 1
Now we shall say that F and G are truth-functionally equivalent if (F ↔ G) is a tautology.
There are other properties of two formulas that we are usually interested in besides truth-functional
equivalence. One of these properties is when two formulas are mutually exclusive. We say two formulas F
and G are mutually exclusive if (F ∧ G) is contradictory (unsatisfiable).
Now using truth tables determine whether the following formulas are truth-functionally equivalent or mutually
exclusive.
(a) p and ¬p
(b) p and ¬¬p
(c) ¬(p ∧ ¬q) and (p → q)
(d) (¬p ∨ q) and (p → q)
(e) ¬(¬p ∨ ¬q) and (p ∧ q)
(f) ¬(¬p ∧ ¬q) and (p ∨ q)
(f) ¬(¬p ∧ ¬q) and (p ∨ q)
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