A University-Level Understanding of Number with an eye towards elementary education

1.

1. It rained yesterday.
   🔗
2. All cars have engines.
   🔗
3. Did you see the game last night?
   🔗
4. All dogs go to Heaven.
   🔗
5. This statement is false.
   🔗
6. Come visit sometime.
   🔗

2.

3.

1. P	Q
   T	T	T
   F	T	F
   T	F	F
   F	F	F

   🔗

2. P	Q
   T	T	T
   F	T	T
   T	F	T
   F	F	F

   🔗

3. P	Q
   T	T	F
   F	T	F
   T	F	F
   F	F	T

   🔗

4. P	Q
   T	T	T
   F	T	T
   T	F	T
   F	F	T

   🔗

4.

1. \(\displaystyle x+3<5\)
   🔗
2. Dog \(D\) is a mastiff.
   🔗
3. Vitamin C helps prevent scurvy.
   🔗
4. The statement \(P\) is both true and false.
   🔗
5. Some countries have kings.
   🔗
6. No one lives in a house.
   🔗

5.

6.

7.

1. The cow is awake and the pig is asleep.
   🔗
2. Stores accept cash or credit as payment.
   🔗
3. Education prepares you for a career or is a poor way to spend your time.
   🔗
4. Anna and Jordan are not happy.
   🔗

8.

1. Gravity is not a force.
   🔗
2. City \(C\) has a population of at least 10 million.
   🔗
3. Harold ate a burger and fries for lunch.
   🔗
4. There is at least one penguin that has never seen Antarctica.
   🔗
5. Everyone on campus is a student or a staff-member.
   🔗
6. No beverage is hot and sweet.
   🔗

9.

1. Peter is not unhappy.
   🔗
2. Not all books are informative or interesting.
   🔗
3. All sculptures are not made of marble.
   🔗
4. No film has sound.
   🔗
5. \(\displaystyle n-2=9\)
   🔗
6. Some buses have 4 tires.
   🔗

10.

1. All parrots are birds.
   🔗
2. Some widgets are gizmos.
   🔗
3. No mountains are volcanoes.
   🔗
4. Songs are not all classical.
   🔗
5. At least one article has no sources.
   🔗
6. Not all athletes have strict diets and exercise every day.
   🔗
7. Some vegans eat honey, but no vegans eat chicken.
   🔗
8. All mammals breathe oxygen, but not all oxygen-breathers are mammals.
   🔗

11.

1. How many rows would be required to construct a truth table for "P and Q or R or S"?
   🔗
2. Construct a truth table for "(P or Q) and R."
   🔗
3. Is "(P or R) and Q" logically equivalent to "(P or Q) and R"? Why or why not?
   🔗

1.

1. When it rains, it pours.
   🔗
2. If you have any snacks left over, can I have them?
   🔗
3. If the stock market crashes, the economy will enter a recession.
   🔗
4. \(c+d\) is even if \(c\) and \(d\) are both multiples of 3.
   🔗
5. Let someone else hold your phone if you’re scared of dropping it.
   🔗
6. If you want to cross the street, then make sure to look both ways for traffic first.
   🔗

2.

3.

1. If the Blue Jays win the World Series, I will eat my hat.
   🔗
2. Sharks die if they stop moving.
   🔗
3. When the weather is cold, the roads are slippery.
   🔗
4. If \(n\) is odd, then it can be written as the sum of an even number and an odd number.
   🔗

4.

1. If \(p\) is prime, then \(p^2\) is odd.
   🔗
2. If \(Q\) is a polygon, then the sum of its interior angles is at least \(360^\circ\text{.}\)
   🔗
3. If person \(A\) speaks both official languages of Canada, then they are bilingual.
   🔗
4. [intentionally left blank in original source]
   🔗

5.

6.

1. If the sky is clear at night, you can see the stars.
   🔗
2. You will excel academically if and only if you study diligently.
   🔗
3. \(2n\) is even exactly when \(n\) is an integer.
   🔗
4. If \(x\) is an integer, then there is exactly one solution to \(x^4=1\text{.}\)
   🔗
5. If an animal is a bird then it has feathers, and if an animal has feathers then it is a bird.
   🔗

7.

1.

1. {a, b, c, d, e, f}
   🔗
2. \(\displaystyle {1, 2, 3, 5, 1, 4}\)
   🔗
3. {Cats, dogs, parrots, goldfish, snakes}
   🔗
4. \(\displaystyle {x ∈ ℤ ∣ x \text{ is prime}}\)
   🔗
5. {I want to go to the park.}
   🔗

2.

1. {All egg-laying mammals}
   🔗
2. {All Canadian provinces}
   🔗
3. \(\displaystyle ∅\)
   🔗
4. {All prime numbers between 10 and 30}
   🔗
5. \(\displaystyle {x ∈ ℚ ∣ |x| < 4}\)
   🔗
6. {Three NHL teams}
   🔗

3.

1. \(\displaystyle A ∪ B\)
   🔗
2. \(\displaystyle B ∩ C\)
   🔗
3. \(\displaystyle A ∩ B ∩ C\)
   🔗
4. \(\displaystyle B - A\)
   🔗

4.

5.

6.

7.

1. \(\displaystyle A = ℤ\)
   🔗
2. \(A = \mathbb{N}_0\) …
   🔗
3. \(A = \mathbb{N}\) …
   🔗
4. \(A = \mathbb{Q}\) …
   🔗

8.

1. \(\displaystyle \{corn, peas, carrots, potatoes, tomatoes, pumpkins\}\)
   🔗
2. \(\displaystyle \{x ∣ x \text{ is a perfect square and } x ≤ 100\}\)
   🔗
3. \(\displaystyle \{x \ | \ x \text{is a two digit natural number with no digit being 7 and } x \leq 100 \}\)
   🔗
4. \(\displaystyle \{40, 45, 50, 55, \ldots, 375, 380, 385 \} \)
   🔗

1.

2.

3.

4.

5.

6.

7.