Given p: Mindanao is an island in the Philippines. q: Find a number which divides your age. r: My seatmate will get a perfect score in the Logic exam. s: Welcome to the Philippines! What is s ^ p

Welcome to the Philippines and Mindanao is an Island in the Philippines.

p: Mindanao is an island in the Philippines. q: Find a number which divides your age. r: My seatmate will get a perfect score in the Logic exam. s: Welcome to the Philippines! What is ¬ r -> q

If my seatmate will not get a perfect score in the logic exam, then find a number which divides your age.

p: Mindanao is an island in the Philippines. q: Find a number which divides your age. r: My seatmate will get a perfect score in the Logic exam. s: Welcome to the Philippines! what is ¬ p v ¬ r

Mindanao is not an island in the Philippines or My seatmate will not get a perfect score in the Logic Exam.

Order of Logical Precedence: 1.) Negation 2.) Disjunction 3.) Conjunction 4.) Implication 5.) Bi-conditional Is this precedence correct?

p -> q becomes q - > p What Related Implications is this?

Converse

p -> q becomes ¬ q - > ¬ p What Related Implications is this?

Contrapositive

p -> q becomes ¬ p - > ¬ q What Related Implications is this?

Inverse

It is any statement that is TRUE regardless of the truth values of the constituent parts

Tautology

It is any statement that is FALSE regardless of the truth values of the constituent parts

Contradiction

It is any statement that is NEITHER a tautology NOR a contradiction

Contingency

These are two (2) different compound propositions that have EXACTLY the SAME/IDENTICAL truth value in every model

Logically Equivalent

Which statement is FALSE about a Proposition

Gives a command

p: Mindanao is an island in the Philippines. q: Find a number which divides your age. r: My seatmate will get a perfect score in the Logic exam. s: Welcome to the Philippines! What is q ⊕ r

Either My seatmate will get a perfect score in the Logic exam or Find a number which divides your age.

p: Mindanao is an island in the Philippines. q: Find a number which divides your age. r: My seatmate will get a perfect score in the Logic exam. s: Welcome to the Philippines! What is p ↔ q

Mindanao is an island in the Philippines if and only if You find a number which divides your age

It is not included in the parenthesis.

Major Connective

Change the statement according to precedence ¬p ^ q

(¬p) ^ q

Change the statement according to precedence p ^ q ^ r ^ s

(p ^ q) ^ r) ^ s)

Change the statement according to precedence p ^ q -> q v p

(p ^ q) -> (q v p)

Change the statement according to precedence p -> q -> r -> s

(p -> (q -> (r -> s)

420 < 69 Is this statement a proposition? If yes, what is the truth value

Yes, False

Please do not run away Is this statement a proposition? If yes, what is the truth value

(p ^ q) -> (q v p) What is the major connective?

(¬p) ^ q What is the major connective?

Prove that p v ¬q is a tautology

It is not a tautology, but a contingency

Prove that (p v q) v [(¬p) ^ (¬q)] is a tautology

It really is a tautology

Prove that p v ¬p is a contradiction

It is not a contradiction, but a tautology

Prove that (p v q) ^ [(¬p) ^ (¬q)] is a contradiction

It really is a contradiction

Prove that q v ¬( p -> q) is a contradiction

It is not a contradiction, but a contingency

Prove that q v ¬( p -> q) is a contradiction

It is not a contradiction, but a contingency