Question

assessment practice

1. write the two conditional statements that make up the following biconditional statement.

two lines are parallel if and only if they do not intersect.

1. sat/act which represents the contrapositive of p → q?

a p ↔ q
b q → p
c ~p → ~q
d ~q → ~p
e ~q ↔ ~p

Explanation:

Step1: Recall biconditional - conditional relationship

A biconditional statement "p if and only if q" is equivalent to two conditional statements: "if p then q" and "if q then p".
Let \(p\) be "Two lines are parallel" and \(q\) be "They do not intersect".
The first conditional statement is: If two lines are parallel, then they do not intersect.
The second conditional statement is: If two lines do not intersect, then they are parallel.

Step2: Recall contra - positive definition

The contra - positive of a conditional statement \(p
ightarrow q\) is \(\sim q
ightarrow\sim p\).

Answer:

36.

• Conditional 1: If two lines are parallel, then they do not intersect.
• Conditional 2: If two lines do not intersect, then they are parallel.

1. D. \(\sim q

ightarrow\sim p\)