Question

1. inverse/contrapositive

a. when taking the inverse we
__________ the hypothesis and
conclusion.

b. for the contrapositive we ____ and ____
the hypothesis and conclusion.

notes:

Explanation:

For part A, in logic (a subfield related to Mathematics, specifically in areas like Algebra or Logic), the inverse of a conditional statement \( p \to q \) is \(
eg p \to
eg q \). So we negate both the hypothesis (\( p \)) and the conclusion (\( q \)).

For part B, the contrapositive of \( p \to q \) is \(
eg q \to
eg p \). So we first swap (or reverse) the hypothesis and the conclusion (i.e., take the converse) and then negate both. So the steps are swap (or reverse) and negate (or we can think of it as negate and swap, but the standard way is to reverse the order and then negate both).

Answer:

s:
A. When taking the inverse we \(\boldsymbol{\text{negate}}\) the hypothesis and conclusion.

B. For the contrapositive we \(\boldsymbol{\text{swap (or reverse)}}\) and \(\boldsymbol{\text{negate}}\) the hypothesis and conclusion (or "negate" and "swap (or reverse)" as the order can be considered in terms of operation: first swap \( p \) and \( q \) to get \( q \to p \), then negate both to get \(
eg q \to
eg p \), so the operations are swap and negate).