---
title: "Contrapositive and inverse: snow statement"
subject: "Discrete Structure"
chapter: 1
key: "semester_4/discrete_structure:contrapositive-inverse-snow-home"
source: https://www.bctengineer.com/q/semester_4/discrete_structure/contrapositive-inverse-snow-home
site: BCT Engineering
---

# Contrapositive and inverse: snow statement

Discrete Structure · Chapter 1: Logic, Induction and Reasoning

- Asked in: 2072 Asoj, 2 marks
- Video: [Converse, Inverse and Contrapositive - Logic - Discrete Mathematics](https://www.youtube.com/watch?v=8JMHAoODFXY) — Ekeeda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/discrete_structure/contrapositive-inverse-snow-home
- Whole chapter: https://www.bctengineer.com/md/semester_4/discrete_structure/chapter-1

## Question

State the contrapositive and inverse of the conditional statement, "If it snows tonight then I will stay at home".

## Short answer

The contrapositive is "If I do not stay at home tonight, then it does not snow tonight." The inverse is "If it does not snow tonight, then I will not stay at home."

## Answer

Let p: "it snows tonight" and q: "I will stay at home". The statement is p → q.

- **Contrapositive** (¬q → ¬p): If I do not stay at home tonight, then it does not snow tonight.
- **Inverse** (¬p → ¬q): If it does not snow tonight, then I will not stay at home.

The contrapositive is equivalent to the original statement; the inverse is not.

## Check yourself

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

1. 'If it snows tonight then I will stay at home' is p → q. What are p and q?
   A. p: stay at home; q: it snows
   B. p: it snows tonight; q: I stay at home
   C. p: it does not snow; q: I stay home
   D. p: stay home; q: no snow
   Answer: B. The antecedent after 'if' is p. (Key point: Symbolic form)

2. Which is the contrapositive?
   A. If it does not snow, I do not stay at home
   B. If I stay at home, it snows
   C. If it snows, I do not stay at home
   D. If I do not stay at home, then it does not snow tonight
   Answer: D. ¬q → ¬p. (Key point: Contrapositive)

3. Which is the inverse, and is it equivalent to the original?
   A. If I stay home, it snows; equivalent
   B. If it does not snow, I will not stay home; equivalent
   C. If I do not stay home, it does not snow; not equivalent
   D. If it does not snow, I will not stay at home; not equivalent
   Answer: D. Inverse ¬p → ¬q is not equivalent to p → q. (Key point: Inverse)

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