Inverses, converses, and contrapositives

1. Two intersecting lines create an angle.
2. If today is Monday, then Kevin will play soccer.
3. If $1+2=3$, then $1^2+2^2=3^2$.
4. If the polygon is a triangle, then it has 3 sides.

1. $r \to s$
2. $p$ $to$ ~$q$
3. ~$m$ $\to$ $n$
4. ~$u$ $\to$ ~$v$

1. If $x+7=13$, then $x=6$.
2. If $3$ is odd, then $3+1$ is even.
3. If $2$ is an integer, then $2$ is a whole number.

1. $p \to q$
2. $q\ to p$
3. ~$q$ $\to$ ~$p$
4. $p$ $\to$ ~$q$

Find the truth value of the following conditionals. Then write the contrapositive and find the truth value of the contrapositive. Are the truth values the same?

1. If (2+3)×4=20, then $2+3=5$.
2. If $4$ is even, then $4+2$ is even.
3. If $3$ is an integer, then $3$ is not a whole number.

Find possible truth values for $p$ and $q$ where:

1. $p \to q$ and ~$q$ $\to$ ~$p$ is both false?
2. $p$ $\to$ $q$ and $q$ $\to$ $p$ is both true?
3. $p \to q$ and $q \to p$ is both false?
4. $q \to p$ and ~$q$ $\to$ ~$p$ is both true?