The conditional statement needs to be clarified before we can write the five conditionals.
See solution.
Practice makes perfect
We need to write the given statement as an if-then statement then write the converse, inverse, contrapositive, and bi-conditional statements. Let's start with the if-then statement.
If-Then
If-then statements take a specific form.
&If p,
&then q.
Here, p is the hypothesis and q is the conclusion. For this exercise, we are told that "4x+9=21 because x=3." Therefore, a logical if-them statement would be as follows.
&If x=3,
&then 4x+9=21.
Converse
When we write the converse, we swap the hypothesis and the conclusion.
&If 4x+9=21,
&then x=3.
Inverse
When we write the inverse, we negate the hypothesis and conclusion in the original conditional statement.
&If x≠3,
&then 4x+9≠21.
Contrapositive
When we write the contrapositive, we negate the hypothesis and conclusion in the converse.
&If 4x+9≠21,
&then x≠3.
Bi-Conditional
Bi-conditional statements use "if and only if" to show that a conditional statement works both ways. Since two lines will always form a point if they intersect, we can write the following bi-conditional statement.
