its symbone Tom. 6) If this is not a herring, then this is not a fish. given that the statements p and q are as indicated p: This is a herring. q: This is a fish. a)-p-q b)-9--P 2 -p-q d) p-q

Advanced Engineering Mathematics
10th Edition
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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**Logical Statements and Symbolic Form**

Given that \( p \) and \( q \) each represent a simple statement, write the indicated compound statement in its symbolic form. 

- **Statements:**
  - \( p \): This is a herring.
  - \( q \): This is a fish.

- **Compound Statements:**

  a) If this is not a herring, then this is not a fish.

     Symbolic form: \(\neg p \rightarrow \neg q\)

  b) \( q \leftrightarrow \neg p \)

  c) \( p \lor \neg q \)

  d) \( p \land q \)

- **Explanation for Diagrams:**

  A logic diagram often involves symbols like:
  - \(\neg\): Not
  - \(\rightarrow\): Implies
  - \(\leftrightarrow\): If and only if
  - \(\lor\): Or
  - \(\land\): And

These symbols are used to create and interpret complex logical statements from basic propositions.
Transcribed Image Text:**Logical Statements and Symbolic Form** Given that \( p \) and \( q \) each represent a simple statement, write the indicated compound statement in its symbolic form. - **Statements:** - \( p \): This is a herring. - \( q \): This is a fish. - **Compound Statements:** a) If this is not a herring, then this is not a fish. Symbolic form: \(\neg p \rightarrow \neg q\) b) \( q \leftrightarrow \neg p \) c) \( p \lor \neg q \) d) \( p \land q \) - **Explanation for Diagrams:** A logic diagram often involves symbols like: - \(\neg\): Not - \(\rightarrow\): Implies - \(\leftrightarrow\): If and only if - \(\lor\): Or - \(\land\): And These symbols are used to create and interpret complex logical statements from basic propositions.
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