Thinking Mathematically Logic 3.2 Compound Statements and Connectives

“Compound” Statements Simple statements can be connected with “and”, “Either … or”, “If … then”, or “if and only if.” These more complicated statements are called “compound.”

Symbolic Logic NameSymbolic Form Read Negation ~p not p Conjunction p/\q p and q Disjunction p\/q p or q

Symbolic Logic (cont.) NameSymbolic FormRead Conditional p  q if p then q p is sufficient for q q is necessary for p Biconditional p  q p if and only if q p is necessary and sufficient for q q is necessary and sufficient for p

Examples Exercise Set 3.2 #3, #7 p: I’m leaving. q: You’re staying. You’re staying and I’m not leaving. p: I study q: I pass the course I study or I pass the course.

Examples Exercise Set 3.2 #11, #23 p: This is an alligator. q: This is a reptile. If this is an alligator, then this is a reptile. p: You are human. q: You have feathers. Being human is sufficient for not having feathers.

Examples Exercise Set 3.2 #35, #49 p: The heater is working q: The house is cold p \/ ~q p: Romeo loves Juliet. q: Juliet loves Romeo. ~(p /\ q)

Dominance of Connectives 1.Negation (~) 2.Conjunction/Disjunction ( /\, \/ ) 3.Conditional (  ) 4.Biconditional (  ) The most dominant is applied last Analogous to order of operations in algebra

Examples Exercise Set 3.2 #59, #79 p: The temperature outside is freezing. q: The heater is working. r: The house is cold. The temperature outside is freezing and the heater is working, or the house is cold. p: The temperature is above 85 o q: We finished studying r: We go to the beach. ~r  ~(p /\ q)

Examples Exercise Set 3.2 #85 I miss class if and only if it’s not true that both I like the teacher and the course is interesting.

Thinking Mathematically Logic 3.2 Compound Statements and Connectives