Write the statement in symbolic form. Then construct a truth table for the symbolic statement. If you do not like the new horror movie then you can leave early, or you can go to another movie. .... Write the statement in symbolic form and construct a truth table for the symbolic statement. Let p = "you like the new horror movie," q = "you can leave early," and r="you can go to another movie." Fill in the blanks below. -p TT T. F F F T F F F F F
Write the statement in symbolic form. Then construct a truth table for the symbolic statement. If you do not like the new horror movie then you can leave early, or you can go to another movie. .... Write the statement in symbolic form and construct a truth table for the symbolic statement. Let p = "you like the new horror movie," q = "you can leave early," and r="you can go to another movie." Fill in the blanks below. -p TT T. F F F T F F F F F
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**Title: Constructing a Truth Table for Symbolic Logic**
**Instructions:**
Write the statement in symbolic form. Then construct a truth table for the symbolic statement.
**Statement:**
"If you do not like the new horror movie then you can leave early, or you can go to another movie."
**Symbolic Form:**
Let \( p \) = "you like the new horror movie,"
\( q \) = "you can leave early,"
\( r \) = "you can go to another movie."
The symbolic statement is: \(\neg p \rightarrow (q \vee r)\).
**Truth Table:**
| \( p \) | \( q \) | \( r \) | \(\neg p\) | \(q \vee r\) | \(\neg p \rightarrow (q \vee r)\) |
|---------|---------|---------|-----------|---------------|-----------------------------------|
| T | T | T | F | T | T |
| T | T | F | F | T | T |
| T | F | T | F | T | T |
| T | F | F | F | F | T |
| F | T | T | T | T | T |
| F | T | F | T | T | T |
| F | F | T | T | T | T |
| F | F | F | T | F | F |
**Explanation:**
The truth table evaluates all possible combinations of truth values for \( p \), \( q \), and \( r \). The table demonstrates the logic of the statement \(\neg p \rightarrow (q \vee r)\), showing when it is true or false. The negation of \( p \), logical OR operation between \( q \) and \( r \), and the implication are calculated for each scenario.
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