---
title: "Converse etc. of beach statement"
subject: "Discrete Structure"
chapter: 1
key: "semester_4/discrete_structure:converse-contrapositive-inverse-beach"
source: https://www.bctengineer.com/q/semester_4/discrete_structure/converse-contrapositive-inverse-beach
site: BCT Engineering
---

# Converse etc. of beach statement

Discrete Structure · Chapter 1: Logic, Induction and Reasoning

- Asked in: 2071 Bhadra, 3 marks
- Video: [Converse, Inverse, & Contrapositive - Conditional & Biconditional Statements, Logic, Geometry](https://www.youtube.com/watch?v=TCBu8PD4Lls) — The Organic Chemistry Tutor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/discrete_structure/converse-contrapositive-inverse-beach
- Whole chapter: https://www.bctengineer.com/md/semester_4/discrete_structure/chapter-1

## Question

State the converse, contrapositive and inverse for the conditional statement, "I go to the beach whenever it is a sunny summer day."

## Short answer

Converse: If I go to the beach then it is a sunny summer day. Contrapositive: If I do not go to the beach then it is not a sunny summer day. Inverse: If it is not a sunny summer day then I do not go to the beach.

## Answer

The statement "q whenever p" means p → q. Let p: "it is a sunny summer day" and q: "I go to the beach". Original: **If it is a sunny summer day, then I go to the beach.**

| Form | Symbolic | Statement |
|---|---|---|
| Converse | q → p | If I go to the beach, then it is a sunny summer day. |
| Contrapositive | ¬q → ¬p | If I do not go to the beach, then it is not a sunny summer day. |
| Inverse | ¬p → ¬q | If it is not a sunny summer day, then I do not go to the beach. |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. 'I go to the beach whenever it is a sunny summer day' means?
   A. If I go to the beach, it is a sunny summer day
   B. If it is a sunny summer day, I go to the beach
   C. I go to the beach only on sunny days
   D. Both directions
   Answer: B. 'q whenever p' means p → q. (Key point: Translating 'whenever')

2. The converse is?
   A. If I go to the beach, then it is a sunny summer day
   B. If it is not sunny, I do not go to the beach
   C. If I do not go to the beach, it is not sunny
   D. If it is sunny, I do not go
   Answer: A. Converse q → p swaps the parts. (Key point: Converse)

3. The inverse is?
   A. If I do not go to the beach, then it is not a sunny summer day
   B. If it is not a sunny summer day, then I do not go to the beach
   C. If it is sunny, I go to the beach
   D. If I go to the beach, it is sunny
   Answer: B. Inverse ¬p → ¬q negates both. (Key point: Inverse)

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