Symbols and statements
Give the correct names of each symbol in order
1. ∅
2. ∃
3. ∀
4. ⊂
5. ∩
1. Empty set
2. existential
3. Universal
4. Subset
5. Intersection
On the board, write down the symbol for logical equivalence and the symbol used in arguments
≡
⇒
A ={2, 4, 6, 8, 10}
What is the word used for a universal quantifier?
BONUS: what is the phrase used with universal quantifiers? (+ 100)
"All"
BONUS: "For every" or "For all"
In the statement " 3 is a whole number"
What is the word to describe "3"?
Term
On the board, draw the symbol for a biconditional statement
↔
How do I show two statements are logically equivalent?
Show their truth values are the same
Given sets
B= {2,4} and D = {2,3,4,6,7}
Is B ⊂ D?
YES
What is the word used for an existential quantifier?
BONUS: what is the phrase used with existential quantifiers? (+ 100)
"Some"
BONUS: "There exists"
In the statement " 3 is a whole number"
What is the word to describe "is a whole number"?
Predicate
Given the statements:
p: Mr. Eldredge is a teacher. q: Monkeys can drive
What is the statement p ∧ ~q in standard form?
Mr. Eldredge is a teacher and Monkeys cannot drive
How do I show an argument is valid?
Show that the first statement implies the second statement (to do this, show that the conditional between the first statement then the second statement is a tautology
Given sets
A = {1,3,5} and B = {3,6,9}
Write on the board A U C
A U C = {1,3,5,6,9}
Write on the board the symbols for quantified statements. First, the symbol for universal quantifiers and then the symbol for Existential quantifiers
Universal- ∀
Existential- ∃
Given the following problem, what word tells me the the number "13" would go in the middle of the venn diagram?
The owner of a toy store wanted to know which toy that he made was the most popular with kids. Of the last 60 sales that were made, a total of 25 people bought stuffed animals, 40 bought race cars, and 13 bought both.
the word "both"
Given the statements:
p: Mr. Eldredge is a teacher. q: Monkeys can drive.
Write on the board the the symbolic version of the following statement:
Monkeys can drive if and only if Mr. Eldredge is not a teacher
q ↔ ~p
Prove (or disprove) the following statements are logically equivalent
(p ↔ ~q) ∧ p ≡ ~q
NOT logically equivalent
Given sets
E = {1,2,5,9} and D = {2,3,4,6,7}
Write on the board E ∩ D
E ∩ D = {2}
"Some Dogs are huskies"
"All dogs are not huskies"
Use a venn diagram to answer the following question
A student wanted to know what lunch food was his grades favorite. Out of the 60 students he asked, a total of 32 said chicken nuggets, a total of 42 said pizza, and 22 said they liked both.
How many students liked only pizza?
20
When learning set theory, Mr. Eldredge talked about Union and Intersection being related to symbols in truth statements. Which were they related to?
Union is related to Disjunction
Intersection is related to Conjunction
Prove (or disprove) the following argument is valid
[p ∧ (p → q)] ⇒ (p ∨ ~q)
Valid
Write on the board two sets, A and B, that would give me the following results
A ∩ B = {∅}
As long as set A and set B have nothing in common, the answer is correct
On the board, convert the following statement into symbolic form
"All turtles are green"
(∀x) (Tx → Gx)
Use a Venn diagram to answer the following question
A principal at an elementary school sent out a survey to the students to find out their favorite activity at recess between playing sports, playing on the playground, or playing games. The following is the results:
Sports.....450
Playground and Games..... 200
Playground only..... 110
Games only....90
Sports and Games but not Playground....150
Playground and Games but not Sports..... 120
Sports only..... 100
None....30
How many people liked to play all three?
80