Inverses, converses, and contrapositives - Logic

Intro Lesson

• a)

  Inverse Statements

• b)

  Converse Statements

• c)

  Contrapositive Statements

• d)

  Logical equivalents

• a)

  Two intersecting lines create an angle.

• b)

  If today is Monday, then Kevin will play soccer.

• c)

  If $1+2=3$, then $1^2+2^2=3^2$.

• d)

  If the polygon is a triangle, then it has 3 sides.

• a)

  $r \to s$

• b)

  $p$ $to$ ~$q$

• c)

  ~$m$ $\to$ $n$

• d)

  ~$u$ $\to$ ~$v$

• a)

  If $x+7=13$, then $x=6$.

• b)

  If $3$ is odd, then $3+1$ is even.

• c)

  If $2$ is an integer, then $2$ is a whole number.

• a)

  $p \to q$

• b)

  $q\ to p$

• c)

  ~$q$ $\to$ ~$p$

• d)

  $p$ $\to$ ~$q$

• a)

  If (2+3)×4=20, then $2+3=5$.

• b)

  If $4$ is even, then $4+2$ is even.

• c)

  If $3$ is an integer, then $3$ is not a whole number.

• a)

  $p \to q$ and ~$q$ $\to$ ~$p$ is both false?

• b)

  $p$ $\to$ $q$ and $q$ $\to$ $p$ is both true?

• c)

  $p \to q$ and $q \to p$ is both false?

• d)

  $q \to p$ and ~$q$ $\to$ ~$p$ is both true?