Symbolic Notation

p: It is raining.

q: The game is cancelled.

If it is raining, then the game is cancelled.

• $p\rightarrow q$

• $q\rightarrow p$

• $p\rightarrow\sim q$

• $\sim p\wedge q$

p: It is raining.

q: The game is cancelled.

If it is not raining, then the game is cancelled.

• $p\rightarrow q$

• $q\rightarrow p$

•  $\sim p\rightarrow q$ 

• $\sim p\wedge q$

Tags

CCSS.HSS.CP.A.5

p: It is raining.

q: The game is cancelled.

It is not raining and the game is cancelled.

• $p\rightarrow q$

• $q\rightarrow p$

•  $\sim p\rightarrow q$ 

• $\sim p\wedge q$

p: It is raining.

q: The game is cancelled.

r: The boy is sad.

If it is raining and the game is cancelled, then the boy is sad.

•  $p\rightarrow q\wedge r$ 

•  $q\rightarrow p\vee r$ 

•  $p\wedge q\rightarrow r$ 

•  $\sim p\wedge q\vee r$ 

p: It is raining.

q: The game is cancelled.

r: The boy is sad.

The game is cancelled and the boy is sad; therefore, it is raining.

•  $q\wedge r\therefore p$  
  

•  $q\vee r\therefore p$  
  

•  $q\rightarrow r\wedge p$  
  

•  $q\wedge\sim r\rightarrow p$  
  

g: The girl runs.
h: The rabbit hops.
j: The girl and the rabbit are having fun.

 $g\vee h$  

• If the girl runs, then the rabbit hops.

• The girl runs and the rabbit hops.

• The girl runs or the rabbit hops.

• If the rabbit hops, then the girl runs.

Tags

CCSS.HSS.CP.A.1

CCSS.HSS.CP.B.7

g: The girl runs.
h: The rabbit hops.
j: The girl and the rabbit are having fun.

 $g\wedge h\rightarrow j$  

• If the girl runs, then the rabbit hops and they are having fun.

• If the girl runs and the rabbit hops. then they are having fun,

• If the girl runs or the rabbit hops, then they are not having fun,

• If the rabbit hops, then the girl runs and they are having fun.

g: The girl runs.
h: The rabbit hops.
j: The girl and the rabbit are having fun.

 $j\therefore g\wedge h$  

• The girl and the rabbit are having fun if the girl runs and the rabbit hops.

• The girl runs and the rabbit hops. therefore, they are having fun,

• If the girl runs and the rabbit hops, then they are having fun,

• The girl and the rabbit are having fun, ,therefore, the girl runs and the rabbit hops.

g: The girl runs.
h: The rabbit hops.
j: The girl and the rabbit are having fun.

 $\sim g\vee\sim h\rightarrow\sim j$  

• If the girl runs or the rabbit doesn't hop, then they are having fun.

• If the girl doesn't run or the rabbit doesn't hop, then they are not having fun.

• If the girl runs and the rabbit hops, then they are having fun,

• If the girl doesn't run and the rabbit doesn't hop, then they are not having fun.

How would you negate this statement:

It is not raining.

• It is not raining.

• It is raining.

• It isn't raining.

• Raining, it is not.

Tags

CCSS.HSS.CP.A.1