Question

use the symbolic notation to write the inverse.

1. write -p→ -q. p: w, x, and y are collinear q: they are on the same line
2. write -p→ -q. p: you are 13 - 19 years old q: you are a teenager
3. write -p→ -q. p: two lines intersect q: they intersect at exactly one point

write the inverse of each statement and then determine the truth - value. if its false, provide a counterexample.

1. if it is october, then there are 31 days this month.
2. if a letter is a consonant, then it is not a, e, i, o, or u.
3. if a triangle is equilateral, then the interior angles are congruent.
4. if two numbers are negative, then the product of the numbers is positive.

write each quote as a conditional statement and then write the inverse of the statement.

1. anyone who has never made a mistake has never tried anything new.
2. live yourself first and everything else falls into line - lucille ball

Explanation:

11.

Step1: Recall inverse form

The inverse of \(p
ightarrow q\) is \(
eg p
ightarrow
eg q\). Given \(p:W, X,\) and \(Y\) are collinear and \(q\): they are on the same line. The inverse \(
eg p
ightarrow
eg q\) is: If \(W, X,\) and \(Y\) are not collinear, then they are not on the same line.

12.

Step1: Identify components

Given \(p\): you are 13 - 19 years old and \(q\): you are a teenager. The inverse \(
eg p
ightarrow
eg q\) is: If you are not 13 - 19 years old, then you are not a teenager.

13.

Step1: Apply inverse rule

Given \(p\): two lines intersect and \(q\): they intersect at exactly one point. The inverse \(
eg p
ightarrow
eg q\) is: If two lines do not intersect, then they do not intersect at exactly one point.

14.

Answer:

Inverse: If it is not October, then there are not 31 days this month. False. Counter - example: January has 31 days.

15.