- Open: Sentence with variable. ex:) x+2=8, It is my favorite color.

- Closed: Sentence without a variable. ex:) 6+2=8, The grass is green.

- They are either true, false, or open.

- They must be closed to be truth/false.

- ex:) True: A square has equal side lengths.

False: A pentagon has 67 sides.

Open: It has a right angle.

- Giving the opposite truth value.

- Symbol ~

Symbols: Representations of sentences, usually in letter form.

ex.) P: I passed my test.

negation: ~P

I did not pass my test.

- And (Conjunction): Two things depend on each other. Symbol: ^.

To be true, both parts must be true.

- Or (Disjunction): Two things do not depend on each other. Symbol: V.

- Examples:

And- C= All cats bark.

E= 7+4=11

C^E (False)

~C^E (True)

C^~E (False)

~E^~C (False)

Or- M= I go to the mall.

B: I buy sneakers.

MVB (True)

~MVB (True)

MV~B (True)

~MV~B (False)

- Distribute the negative.

- Flip the sign.

- Symbol:  ~.

- Ex.) ~(P^Q) : ~PV~Q

~(~CVB) : C^~B

- Means to imply.

- A compound sentence.

- Every action has a reaction.

- Parts of the sentence:

*hypothesis- Sentence or phrase that starts with "if."

*conclusion- Sentence or phrase that starts with "then."

ex.) If I eat a lot of icecream, then I get a brainfreeze.

- Symbol:  ->

ex.) P: I go on a field trip, W: I miss schoolwork.

P->W  (Truth Value- T->T equals T)

P   Q    P-> Q

                          T    T         T

                          T    F         F

                          F    T         T

                          F    F         T

- If and only if.

- Symbol: <-->.

ex.) P: A triangle is isosceles. (T)

Q: A triangle has 2 congruent sides. (T)

P <--> Q (T)

P     Q   P<-->Q

                         T     T        T
                         T     F        F
                         F     T        F
                         F     F        T

- Changing the truth value of the conditional.

- Change the sign.

- ex.) If I like chocolate, then I eat kisses.

If I do not like chocolate, then I do not eat kisses.

- Changing the order of the conditional.

- Change order.

- ex.) If I put on shoes, then I tie my shoes.

If I tie my shoes, then I put on my shoes.

- Logically equilvilant.

- Change the order and the sign.

- Same truth value.

- ex.) If I get married, then I say I do.

If I do not say I do, then I do not get married.