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

# Converse etc. of temple statement

Discrete Structure · Chapter 1: Logic, Induction and Reasoning

- Asked in: 2074 Bhadra, 3 marks
- Video: [Converse, Inverse, Contrapositive, Biconditional Statements](https://www.youtube.com/watch?v=4yfDM5zV6H4) — Mario's Math Tutoring
- 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-temple-saturday
- Whole chapter: https://www.bctengineer.com/md/semester_4/discrete_structure/chapter-1

## Question

Write the inverse, converse and contrapositive of the statement "I visit temple only if it's Saturday".

## Short answer

Let p: I visit temple, q: it's Saturday. The statement 'p only if q' is p→q. Converse: q→p (If Saturday, I visit). Inverse: ¬p→¬q (If I don't visit, it's not Saturday). Contrapostive: ¬q→¬p (If not Saturday, I don't visit).

## Answer

Let p: "I visit the temple" and q: "it is Saturday". "p only if q" means **p → q**: if I visit the temple, then it is Saturday.

| Form | Symbolic | Statement |
|---|---|---|
| Converse | q → p | If it is Saturday, then I visit the temple. |
| Inverse | ¬p → ¬q | If I do not visit the temple, then it is not Saturday. |
| Contrapositive | ¬q → ¬p | If it is not Saturday, then I do not visit the temple. |

Only the contrapositive is logically equivalent to the original statement.

## Check yourself

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

1. 'I visit temple only if it is Saturday' is?
   A. If it is Saturday then I visit the temple
   B. If I visit the temple then it is Saturday
   C. I visit the temple and it is Saturday
   D. If I do not visit the temple then it is not Saturday
   Answer: B. 'p only if q' is p → q. (Key point: Symbolising)

2. The contrapositive is?
   A. If it is Saturday, I visit the temple
   B. If it is not Saturday, I do not visit the temple
   C. If I do not visit the temple, it is not Saturday
   D. If I visit the temple, it is not Saturday
   Answer: B. ¬q → ¬p. (Key point: Contrapositive)

3. The inverse is?
   A. If it is not Saturday, I do not visit the temple
   B. If it is Saturday, I visit the temple
   C. If I do not visit the temple, then it is not Saturday
   D. If I visit the temple, it is Saturday
   Answer: C. Inverse ¬p → ¬q negates both parts without swapping. (Key point: Inverse)

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