Let p = "2 is a factor of n," q = "3 is a factor of n," and r= "6 is a factor of n." (a) Let Statement A be "If 2 is a factor of n and 3 is a factor of n, then 6 is a factor of n." Which of the following expresses Statement A in symbolic form? Opva Opnar Opvar O~P~g →r Opn~g (b) Let Statement B be "2 is not a factor of n, or 3 is not a factor of n, or 6 is a factor of n." Which of the following expresses Statement B in symbolic form? ONDANG Ar O p V NT O~Par ONDANG →r O ~p V NQ vr (c) Fill in the values in the truth table for Statements A and B. par TTT NP ? ♥ T FT ? ✓ FTF TTF ??✔ TFF FT T ? ♥ ? ✓ Ng ? ✓ ? ✓ ? ✓ ?v ? ✓ ? ✔ FFT ??✔ F FF ? ✓ ?✔ P^q ? ✔ ? ✓ ? V ? V ? ✓ Pлq→r NP V Nq Vr ? ✓ ?✔ ? ✓ ? ✓ ? ✔ ? ✔ ? V ? ✓ ?v ?v ?v ? ✓ Are Statements A and B logically equivalent? Fill in the blanks in the sentences below to justify your answer. The truth table shows that p^grand ~p V ~g vr--Select--- ✓have the same truth values. Therefore, Statements A and B ---Select-- logically equivalent.
Let p = "2 is a factor of n," q = "3 is a factor of n," and r= "6 is a factor of n." (a) Let Statement A be "If 2 is a factor of n and 3 is a factor of n, then 6 is a factor of n." Which of the following expresses Statement A in symbolic form? Opva Opnar Opvar O~P~g →r Opn~g (b) Let Statement B be "2 is not a factor of n, or 3 is not a factor of n, or 6 is a factor of n." Which of the following expresses Statement B in symbolic form? ONDANG Ar O p V NT O~Par ONDANG →r O ~p V NQ vr (c) Fill in the values in the truth table for Statements A and B. par TTT NP ? ♥ T FT ? ✓ FTF TTF ??✔ TFF FT T ? ♥ ? ✓ Ng ? ✓ ? ✓ ? ✓ ?v ? ✓ ? ✔ FFT ??✔ F FF ? ✓ ?✔ P^q ? ✔ ? ✓ ? V ? V ? ✓ Pлq→r NP V Nq Vr ? ✓ ?✔ ? ✓ ? ✓ ? ✔ ? ✔ ? V ? ✓ ?v ?v ?v ? ✓ Are Statements A and B logically equivalent? Fill in the blanks in the sentences below to justify your answer. The truth table shows that p^grand ~p V ~g vr--Select--- ✓have the same truth values. Therefore, Statements A and B ---Select-- logically equivalent.
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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Question
![Let \( p = \) "2 is a factor of \( n \)", \( q = \) "3 is a factor of \( n \)", and \( r = \) "6 is a factor of \( n \)."
**(a)** Let Statement A be "If 2 is a factor of \( n \) and 3 is a factor of \( n \), then 6 is a factor of \( n \)." Which of the following expresses Statement A in symbolic form?
- \( p \lor q \)
- \( p \land q \rightarrow r \)
- \( p \lor q \rightarrow r \)
- \( \neg p \land q \rightarrow r \)
- \( p \land \neg q \)
**(b)** Let Statement B be "2 is not a factor of \( n \), or 3 is not a factor of \( n \), or 6 is a factor of \( n \)." Which of the following expresses Statement B in symbolic form?
- \( \neg p \land \neg q \land r \)
- \( p \lor \neg r \)
- \( \neg p \lor r \)
- \( \neg p \land \neg q \rightarrow r \)
- \( \neg p \lor \neg q \lor r \)
**(c)** Fill in the values in the truth table for Statements A and B.
\[
\begin{array}{ccccccc}
p & q & r & \neg q & p \land q & p \land q \rightarrow r & \neg p \lor \neg q \lor r \\
\hline
T & T & T & & & & \\
T & T & F & & & & \\
T & F & T & & & & \\
T & F & F & & & & \\
F & T & T & & & & \\
F & T & F & & & & \\
F & F & T & & & & \\
F & F & F & & & & \\
\end{array}
\]
**Question:** Are Statements A and B logically equivalent? Fill in the blanks in the sentences below to justify your answer.
The truth table shows that \( p \land q \rightarrow r \) and \( \neg p \lor \neg q \lor r \) \_\_\_\_\_ have the same truth values](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7cff8c4a-bb33-4b54-bd2d-8ccd43ef3f82%2F73519185-20ac-42b4-8651-13ae430baef2%2Fth584xx_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( p = \) "2 is a factor of \( n \)", \( q = \) "3 is a factor of \( n \)", and \( r = \) "6 is a factor of \( n \)."
**(a)** Let Statement A be "If 2 is a factor of \( n \) and 3 is a factor of \( n \), then 6 is a factor of \( n \)." Which of the following expresses Statement A in symbolic form?
- \( p \lor q \)
- \( p \land q \rightarrow r \)
- \( p \lor q \rightarrow r \)
- \( \neg p \land q \rightarrow r \)
- \( p \land \neg q \)
**(b)** Let Statement B be "2 is not a factor of \( n \), or 3 is not a factor of \( n \), or 6 is a factor of \( n \)." Which of the following expresses Statement B in symbolic form?
- \( \neg p \land \neg q \land r \)
- \( p \lor \neg r \)
- \( \neg p \lor r \)
- \( \neg p \land \neg q \rightarrow r \)
- \( \neg p \lor \neg q \lor r \)
**(c)** Fill in the values in the truth table for Statements A and B.
\[
\begin{array}{ccccccc}
p & q & r & \neg q & p \land q & p \land q \rightarrow r & \neg p \lor \neg q \lor r \\
\hline
T & T & T & & & & \\
T & T & F & & & & \\
T & F & T & & & & \\
T & F & F & & & & \\
F & T & T & & & & \\
F & T & F & & & & \\
F & F & T & & & & \\
F & F & F & & & & \\
\end{array}
\]
**Question:** Are Statements A and B logically equivalent? Fill in the blanks in the sentences below to justify your answer.
The truth table shows that \( p \land q \rightarrow r \) and \( \neg p \lor \neg q \lor r \) \_\_\_\_\_ have the same truth values
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