True and False Statements

Show your work for each problem.

1.
Which of these is a TRUE statement?
1. a)
2. b)
3. c)
4. d)
Answer:
is true because 5 plus 3 equals 8. The other statements show incorrect sums.
2.
Which of these is NOT a statement?
1. a)
2. b)What is 7 + 2?
3. c)
4. d)A triangle has 3 sides
Answer: What is 7 + 2?
"What is 7 + 2?" is a question, not a statement. Questions ask for information and cannot be true or false. The other options are all statements (either true or false).
3.
Is the statement "" true or false? (Type: true or false)
Answer: true
is TRUE because 12 minus 5 equals 7.
4.
Is the statement "" true or false? (Type: true or false)
Answer: false
is FALSE because , not 25.
5.
Evaluate whether "" is true or false.
Answer: true
1. What does the left side of the equation equal? Calculate . 15
2. What does the right side of the equation show? 15
3. Are both sides equal? (yes or no) yes
4. So is the statement true or false? true
6.
Determine if "" is true or false.
Answer: false
1. What does the symbol mean? greater than
2. Is 8 larger than 12? no
3. So is the statement true or false? false
7.
Which sentence is a statement?
1. a)How many sides does a square have?
2. b)A hexagon has 6 sides.
3. c)Wow, that's amazing!
4. d)Count to ten!
Answer: A hexagon has 6 sides.
"A hexagon has 6 sides" is a statement - it's TRUE and makes a clear claim. Commands ("Count to ten!"), questions ("How many sides..."), and exclamations ("Wow!") are not statements.
8.
Which of these statements is FALSE?
1. a)A circle has no corners.
2. b)
3. c)All rectangles are squares.
4. d)All squares are rectangles.
Answer: All rectangles are squares.
"All rectangles are squares" is FALSE. A rectangle can have sides of different lengths (like 3 cm by 5 cm), so not all rectangles are squares. However, all squares ARE rectangles because they have 4 right angles.
9.
Is the statement "" true or false? (Type: true or false)
Answer: true
is TRUE. The symbol means 'less than or equal to'. Since 20 equals 20, the statement is true.
10.
Is "Close the door" a statement? (Type: yes or no)
Answer: no
"Close the door" is NOT a statement. It is a command (imperative sentence). Commands tell someone to do something and cannot be true or false.
11.
Evaluate the statement: ""
Answer: false
1. Calculate . What is the result? 21
2. The statement says . Is 21 equal to 20? no
3. So is the statement true or false? false
12.
Which statement is TRUE?
1. a)Every number divisible by 2 is divisible by 4.
2. b)Every even number is divisible by 2.
3. c)Zero is a positive number.
4. d)All prime numbers are odd.
Answer: Every even number is divisible by 2.
"Every even number is divisible by 2" is TRUE by definition of even numbers. The others are false: 6 is divisible by 2 but not 4; 2 is a prime number but even; zero is neither positive nor negative.
13.
Is the statement "The sum of two odd numbers is always even" true or false?
Answer: true
This is TRUE! When you add two odd numbers, the result is always even. Examples: , , . All results are even numbers.
14.
Evaluate: "If a number ends in 0, it is divisible by 5."
Answer: true
1. Think of a number that ends in 0. Try 10. Is a whole number? yes
2. Try another: Is a whole number? yes
3. Try 100. Is a whole number? yes
4. All numbers ending in 0 are divisible by 5. Is the statement true or false? true
15.
Is the statement "All multiples of 6 are also multiples of 3" true or false?
Answer: true
1. List some multiples of 6: 6, 12, 18, 24. Is 6 divisible by 3? yes
2. Is 12 divisible by 3? yes
3. Is 18 divisible by 3? yes
4. Since 6 = 2 × 3, any multiple of 6 is also a multiple of 3. Is the statement true or false? true