Certainly! Here's the transcribed text suitable for an educational website:---### Logic and Truth Tables**Problem 5: Creating a Truth Table**Suppose you wish to create a truth table to analyze an argument whose variables are: \( A, B, C, R, S, Q \). How many rows do you have to create to make a truth table?**Problem 6: Logical Equivalence**Create a truth table to determine whether the following symbolic statements are logically equivalent:1. \(\sim ((P \land Q) \lor S)\)2. \((\sim P \lor Q) \land \sim S\)---### Explanation:**Problem 5** involves determining the number of rows in a truth table based on the number of variables. For a set of \( n \) variables, a truth table contains \( 2^n \) rows to account for all possible combinations of truth values (True or False) for each variable.**Problem 6** requires constructing a truth table to compare two logical expressions and check for logical equivalence. This involves evaluating both expressions for each possible combination of truth values of the variables \( P \), \( Q \), and \( S \), and comparing their outcomes. If the columns of truth values for both expressions are the same in every row, the expressions are logically equivalent.

Answered: (5) Suppose you wish to create a truth…

(5) Suppose you wish to create a truth table to analyze an argument whose variables are: A, B, C, R, S, Q, how many rows do you have to create to make a truth table?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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---

### Logic and Truth Tables

**Problem 5: Creating a Truth Table**

Suppose you wish to create a truth table to analyze an argument whose variables are: \( A, B, C, R, S, Q \). How many rows do you have to create to make a truth table?

**Problem 6: Logical Equivalence**

Create a truth table to determine whether the following symbolic statements are logically equivalent:

1. \(\sim ((P \land Q) \lor S)\)
2. \((\sim P \lor Q) \land \sim S\)

---

### Explanation:

**Problem 5** involves determining the number of rows in a truth table based on the number of variables. For a set of \( n \) variables, a truth table contains \( 2^n \) rows to account for all possible combinations of truth values (True or False) for each variable.

**Problem 6** requires constructing a truth table to compare two logical expressions and check for logical equivalence. This involves evaluating both expressions for each possible combination of truth values of the variables \( P \), \( Q \), and \( S \), and comparing their outcomes. If the columns of truth values for both expressions are the same in every row, the expressions are logically equivalent.

Expert Solution

Step 1

HERE AS PER GUIDELINES I HAVE CALCULATED FIRST MAIN QUESTION ONLY PLZ REPOST FOR REMAINING...

here use counting principle .

There are 2 choices for each variable .

nC_r = (n!)/(n-r)!×r!

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