Question

Conditional Statements and Equivalence Quiz

Given the original statement If a number is negative, the additive inverse is positive, which are true? Select three options.
a) If p = a number is negative and q = the additive inverse is positive, the original statement is p - q.
b) If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is p~9.
c) If p = a number is negative and q = the additive inverse is positive, the converse of the original statement is ~ - ~p.
d) If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is - -.
e) If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is 9 - p.

Answer 1

Only option (e) correctly represents a logical operation, the converse, on the original conditional statement by switching 'a number is negative' (q) and 'the additive inverse is positive' (p). The other options are incorrect or unclear as presented.

Step-by-step explanation:

The original statement 'If a number is negative, the additive inverse is positive' can be represented as a conditional statement: If p (a number is negative), then q (the additive inverse is positive). We can then discuss the related logical statements:

• The inverse would negate both the hypothesis and the conclusion: If not p, then not q.
• The converse would switch the hypothesis and the conclusion: If q, then p.
• The contrapositive would negate and switch the hypothesis and conclusion: If not q, then not p.

Given the options in the question:

1. Option (b) refers to an 'inverse' which does not follow the required structure and is therefore incorrect.
2. Option (c) incorrectly attempts to represent the 'converse' but instead uses negation symbols instead of properly using the terminology and symbols.
3. Option (e) correctly represents the 'converse' by switching the places of p and q.

Even though there's a request to ignore typos, options (a), (b), (c), and (d) include symbols or notations that do not correspond to standard representations of the inverse, converse, or contrapositive and are incorrect or unclear as presented. As such, option (e) is the only one that correctly represents one of the logical operations applied to the original statement.