**10. Write a valid conclusion for each argument****A)** \[ a \leftrightarrow b \] \[\sim a \]**B)** \[ a \rightarrow b \] \[ a \]**C)** \[ a \land b \] **Explanation**: - **A)** involves a biconditional statement ($a \leftrightarrow b$), meaning $a$ if and only if $b$, and $\sim a$ (not $a$) indicating that $a$ is false. - **B)** features an implication ($a \rightarrow b$), meaning if $a$ then $b$, with $a$ being true.- **C)** includes a conjunction ($a \land b$), representing $a$ and $b$ together. In each part, the task is to deduce a logical conclusion based on the given premises.

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Description: **10. Write a valid conclusion for each argument****A)** \[ a \leftrightarrow b \] \[\sim a \]**B)** \[ a \rightarrow b \] \[ a \]**C)** \[ a \land b \] **Explanation**: - **A)** involves a biconditional statement ($a \leftrightarrow b$), me

(a). For the given argument a↔b~a--- Since the first argument is a is implies and implied by b and…

Answered: 10. Write a valid conclusion for each…

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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**10. Write a valid conclusion for each argument**

**A)**
\[
a \leftrightarrow b
\]
\[
\sim a
\]

**B)**
\[
a \rightarrow b
\]
\[
a
\]

**C)**
\[
a \land b
\]

**Explanation**:

- **A)** involves a biconditional statement ($a \leftrightarrow b$), meaning $a$ if and only if $b$, and $\sim a$ (not $a$) indicating that $a$ is false.

- **B)** features an implication ($a \rightarrow b$), meaning if $a$ then $b$, with $a$ being true.

- **C)** includes a conjunction ($a \land b$), representing $a$ and $b$ together.

In each part, the task is to deduce a logical conclusion based on the given premises.

Expert Solution

Step 1

(a).

For the given argument

$a \leftrightarrow b ~ a - - -$

Since the first argument is a is implies and implied by b and the second argument is not a.

Therefore, the final conclusion will be $~ b$

(b).

The given argument is

$a \to b a - - -$

Here we know a and a is implying b then the final conclusion will be b by using Modus Ponen.

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