/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 Construct a truth table for the ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 2

Construct a truth table for the given statement. \(\sim p \rightarrow q\)

Short Answer

Expert verified
The truth table for \( \sim p \rightarrow q \) is: (1,1) -> 1, (1,0) -> 0, (0,1) -> 1, (0,0) -> 1. Or in terms of true (T) and false (F): (T,T) -> T, (T,F) -> F, (F,T) -> T, (F,F) -> T.

Step by step solution

01

Define Logical Variables

First, define two logical variables: p and q. As they are logical variables, each of them can take one of two values: true or false. In a truth table, these are often represented as 1 for true and 0 for false.
02

Generate Combinations

Next, generate all possible combinations for the variables p and q. Since there are two variables and each of them can take two values, there will be \(2^2 = 4\) combinations: 1,1; 1,0; 0,1 and 0,0.
03

Calculate not p (Negation of p)

Now, calculate values for \( \sim p \) (not p). According to the negation operator, when p is true (\( p = 1 \)), \( \sim p \) is false (\( \sim p = 0 \)). Similarly, when p is false (\( p = 0 \)), \( \sim p \) is true (\( \sim p = 1 \)). Thus, for the values of p (1,1,0,0), you will get \( \sim p \) as (0,0,1,1).
04

Calculate \( \sim p \rightarrow q \) (not p implies q)

Finally, calculate values for \( \sim p \rightarrow q \) using the implication operator. For the operator \( \rightarrow \), the expression \( p \rightarrow q \) is false only when p is true (p = 1) and q is false (q = 0). In all other cases, it's true. Hence, for the combination of \( \sim p \) and q, the result would be true, false, true and true respectively.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Exercises 43-50, use the standard forms of valid arguments to draw a valid conclusion from the given premises. If a person is a chemist, then that person has a college degree. My best friend does not have a college degree. Therefore, ...

Use Euler diagrams to determine whether each argument is valid or invalid. All comedians are funny people. Some comedians are professors. Therefore, some funny people are professors.

Use the standard forms of valid arguments to draw a valid conclusion from the given premises. If all electricity is off, then no lights work. Some lights work. Therefore, ...

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. $$ \begin{aligned} &p \rightarrow q \\ &\underline{q \rightarrow r} \\ &\therefore \sim p \rightarrow \sim r \end{aligned} $$

Use Euler diagrams to determine whether each argument is valid or invalid. All clocks keep time accurately. All time-measuring devices keep time accurately. Therefore, all clocks are time-measuring devices.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.