Write the Following Compound Statement in Symbolic Form | Logic & Symbolic Representation | Query Point Official

Write the Compound Statement in Symbolic Form and Find Its Converse, Inverse, and Contrapositive

Statement

If I like the teacher or the course is interesting, then I do not miss class.

Solution

Let:

• P = I like the teacher
• Q = The course is interesting
• R = I miss class

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Symbolic Form

(P ∨ Q) → ¬R

This represents: If I like the teacher OR the course is interesting, then I do NOT miss class.

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Converse

¬R → (P ∨ Q)

If I do not miss class, then I like the teacher or the course is interesting.

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Inverse

¬(P ∨ Q) → R

If I do not like the teacher and the course is not interesting, then I miss class.

Note: By De Morgan’s Law,
¬(P ∨ Q) = ¬P ∧ ¬Q

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Contrapositive

R → ¬(P ∨ Q)

If I miss class, then I do not like the teacher and the course is not interesting.

Using De Morgan’s Law:
R → (¬P ∧ ¬Q)

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Important Note

The contrapositive is logically equivalent to the original statement, while the converse and inverse are logically equivalent to each other.

Frequently Asked Questions (FAQs)

1. What does “symbolic form” mean?

Symbolic form refers to expressing logical or mathematical statements using symbols instead of full English sentences. This helps make arguments precise and easier to analyse.

2. Why do we use symbols like ∧ and ∨?

These symbols represent logical connections (AND, OR) that help shorten statements and make them easier to manipulate in proofs or computer logic.

3. Can every English sentence be written in symbolic logic?

Most structured logical statements can be translated into symbols if they contain clear logical connections such as “and”, “or”, “if…then”, or “not”. Ambiguous sentences may require rewriting for clarity first.

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