Statements and Truth values
What is a statement?
A declarative sentence that is either true or false but not both
Conjunctions are truth if and only if both statements are _____
True
Complete the following logical equivalency
~(p ∧ q) ≡
~(p ∧ q) ≡ ~p ∨ ~q
A statement is a contradiction if it is always ____
What NFL quarterback holds the record for most Superbowl wins?
Tom Brady
Which of the following is a Statement
A) Go to your room
B) Achoo!!!
C) A square has seven sides
C) a square has seven sides
Conditional statements are always true EXCEPT when the antecedent is ________ and the consequent is _____________
True, False
What is the name of this logical equivalency
~(~p) ≡ p
Double negation
p implies q if and only if p → q is a ___________
Tautology
As you know, Mr. Eldredge plays football for Utah Tech. What position (specifically) does he play?
Center
Negating a statement changes what?
It's truth value
Which logical operator uses the phrase "If and only if"?
Biconditional
TRUE OR FALSE
Conditionals are commutative
ie: p → q ≡ q → p
FALSE
How do you prove an argument is valid (or how do you show p implies q)?
show that the conditional p → q is a tautology
Who is Mr. Eldredge's favorite class?
TRICK QUESTION!!!
I don't have favorites
What is the negation of the following statement?
Utah Tech University is not in St. George, Utah
Utah Tech University is in St. George, Utah
State the correct logical operators in order according to their signs
1. ∨
2. →
3. ∧
4. ↔
5. ~
1. Disjunction
2. Conditional
3. Conjunction
4. Biconditional
5. Negation
Given the conditional statement p → q; and considering the converse, inverse, and contrapositive; which of these statements are logically equivalent?
Conditional and Contrapositive
Converse and Inverse
Prove (or disprove) the following is an implication
[(p → q) ∨ q] ⇒ p
NOT an implication
What is Mr. Eldredge's majoring in?
Mathematics Teacher Education
Is the following sentence a statement? why or why not?
"Tom Brady is the greatest football player of all time"
Given statement p, which logical operator can make the compounded statement p __ ~p a tautology and which logical operator can make p __ ~p a contradiction?
A disjunction can make p ∨ ~p a tautology and a conjunction can make p ∧ ~p a contradiction
Demorgans Laws
Prove (or disprove) the following argument is valid
[(p ↔ q) ∧ ~p] ⇒ ~q
The argument is valid
The "Shot Heard 'Round the World" was a walk-off home run hit by New York Giants outfielder and third baseman Bobby Thomson off Brooklyn Dodgers pitcher Ralph Branca at the Polo Grounds in New York City on October 3, 1951, to win the National League (NL) pennant. What future hall of fame baseball player was on deck for the New York Giants?
Willie Mays