Conjectures/Counter ex.
Find the next 5 terms of a sequence, then write a conjecture.
1, 4, 9, 16, __, __, __, __, __
What is...
25, 36, 49, 64, 81
Each term is a square. To find the nth term, square n.
Write the compound statement and determine the truth value.
p^r
p: There are 7 days in a week.
q: March has 30 days.
r: Halloween is on October 31st.
What is...
There are 7 days in a week and Halloween is on October 31st.
True.
Write this statement as conditional.
An obtuse angle has a measure greater than 90 degrees.
What is...
If an angle is obtuse, then it has an angle greater than 90 degrees.
Give a conclusion for this given:
If Logan eats his vegetables, he can have a bowl of ice cream.
Logan eats his vegetables.
What is...
Logan can have a bowl of ice cream.
Given: 3x = x + 12
Prove: x=6
What is...
1. 3x = x+ 12 1. Given
2. 2x = 12 2. Subtraction Property
3. x = 6 3. Division Property
Find the next 5 terms, then write a conjecture.
3, 1, 4, 1, 5, __, __, __, __, __
What is...
9, 2, 6, 5, 3
Each term is a digit of pi. To find the nth term, find the nth digit of pi.
Write the compound statement and determine the truth value.
~p^q
p: There are 7 days in a week.
q: March has 30 days.
r: Halloween is on October 31st.
What is...
There are not 7 days in a week, and March has 30 days.
False.
Write this statement in inverse form. Give the truth value.
If the product of two numbers is odd, then both numbers must be odd.
What is...
If the product of two numbers is even, both numbers must be even.
False; 2 x 3 = 6
Write the conclusion for this given:
If it is raining, then I will bring my umbrella.
If I do not bring my umbrella, then I do not need my rainboots.
What is...
Invalid
Given: 2x - 10 = 20
Prove: x = 15
What is...
1. 2x - 10 = 20 1. Given
2. 2x = 30 2. Addition Property
3. x = 15 3. Division Property
True or False?
If false, provide a counterexample.
The sum of any two consecutive integers is always odd.
What is...
True
Write the compound statement and determine the truth value.
~p v ~q
p: There are 7 days in a week.
q: March has 30 days.
r: Halloween is on October 31st.
What is...
There are not 7 days in a week or March does not have 30 days.
True.
Write the converse and truth value of this statement:
If it is Saturday, then there is no school.
What is...
If there is no school, then it is Saturday.
False; Sunday.
What is the conclusion for this given:
If a natural number ends in 0, then it is divisible by 10.
If a natural number is divisible by 10, then it is divisible by 5.
What is...
If a natural number ends in 0, then it is divisible by 5.
Given: x/2 + 5 = 12
Prove: x = 14
What is...
1. x/2 + 5 = 12 1. Given
2. x/2 = 7 2. Subtraction Property
3. x = 14 3. Multiplication Property
True or false?
If false, provide a counterexample.
The product of two numbers is always larger than either number.
What is...
False; 2 x 1/2 = 1
Make a truth table for the equation:
(~p v q) ^ ~r
What is...
p | q | r | ~p | ~r | ~p v q | (~p v q) ^ ~r
____________________________________________ T T T F F T F
T T F F T T T
T F T F F F F
T F F F T F F
F T T T F T F
F T F T T T T
F F T T F T F
F F F T T T T
Write the contrapositive form and truth value of this statement:
If you live in Dallas, then you live in Texas.
What is...
If you don't live in Texas, you don't live in Dallas.
True.
What law is used in this statement?
Given: If you leave the country, then you will need a passport.
Given: Nate is planning a trip to Italy.
Conclusion: Nate will need a passport.
What is...
Law of detachment
D. __________E.__________.F
Given: E is the midpoint of DF
Prove 2DE = DF
What is...
1. E is the midpoint of DF 1. Given
2. DE = EF 2. Definition of midpoint
3. DE + DE = DE + EF 3. Addition Property
4. 2DE = DE + EF 4. Simplify
5. DE + EF = DF 5. Segment Addition Postulate
6. 2DE = DF 6. Transitive Property
True or false?
If false, give counterexample.
For any two integers, a and b, (a+b)2 =a2+b2
What is...
False; (2+3)2=25; 22+32=13
Make a truth table for this equation:
p v ~r
What is...
p r ~r p v ~r
___________________
T T F T
T F T T
F T F F
F F T T
Write the bi-conditional form and truth value of this statement:
If a number is a natural number, then it is also a whole number.
What is...
A number is a natural number if and only if it is also a whole number.
False; converse is false.
What law is used in this statement?
Given: If you are at least 18 year sold, then you can apply for a credit card.
Given: Kelly applied for a credit card.
Conclusion: Kelly is at least 18 years old.
What is...
Invalid
Given: 3(2x + 1) + 2(2x + 1) + 7 = 42 - 5x
Prove: x = 2
What is...
1. 3(2x + 1) + 2(2x + 1) + 7 = 42 - 5x 1. Given
2. 5(2x + 1) +7=42 - 5x 2.Simplify(combine terms)
3. 5(2x + 1) = 35 - 5x 3. Subtraction Property
4. 10x + 5 = 35 - 5x 4. Distibutive Property
5. 15x + 5 = 35 5. Addition Property
6. 15x = 30 6. Subtraction Property
7. x = 2 7. Division Property