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CTJan27 Online Year 8 Numerical Reasoning Counter Examples and Deductive Reason

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1.

Which of the following is an example for the  statement?

You would do better on this quiz if you understood this lecture.
 a. Understanding the lecture but receiving a 10% on the quiz d. Understanding the lecture and achieving a perfect score on the quiz b. I didn't understand the lecture and  got 20% on the quiz e. None c. Not understanding the lecture and receiving a 0 on the quiz

2.

Which of the following numbers is a counterexample to this statement?

All prime numbers are odd.
 a. 2 d. 0 b. 3 e. None c. 8

3.

Provide a counterexample for the proposition:

All numbers are either prime or composite.
 a. 0 d. 42 b. 2 e. None c. 23

4.

The number 22 is a counterexample for which of the following conditional statements?
 a. All numbers devisible by 2 are even d. Product of two prime numbers are even. b. All numbers devisible by 2 are also divisible by 4 e. None c. All multiples of 2 are even.

5.

Which of the following numbers is a counterexample to this statement?

If a number is composite, then it ends with 2,4,6,8 or 0.
 a. 02 d. 10020 b. 04 e. None c. 42

6.

Which of the following numbers is a counterexample to this statement?

The sum of two prime numbers is even.
 a. 7+31 d. 233+3 b. 5+51 e. 2+233 c. 13+3 f. None

7.

Which of the following numbers is a counterexample to this statement? if a. d. b. e. None c. 8.

Which of the following is a counterexample to this statement? is odd for all if q is an integer.

 a. d. b. e. None c. 9.

Which of the following is a counterexample to this statement? for all the integer values of  y .
 a. d. b. e. None c. 10.

Which of the following is a counterexample to this statement? for all the integer values of  x .
 a. d. b. e. None c. 11.

Which of the following is a counterexample to this statement? is always composite for all the integer values of  y except for 1.
 a. d. b. e. None c. 12.

Which of the following is a counterexample to this statement? is always composite for all the integer values of  q except for 1.
 a. d. b. e. None c. 13.

Which of the following is a counterexample to this statement?

if . x always is greater than p.
 a. d. b. e. None c. 14.

Which of the following is a counterexample to this statement?

If a fraction of a numerator is a multiple 2, then the fraction can be simplified.
 a. c. b. d. 15.

Which of the following is a counterexample to this statement?

If a man's work requires him to use a camera, he is a photographer.
 a. A doctor who does not use a camera to do his job. d. When working, an engineer uses his camera to take a selfie. b. A photograper who uses his camera regularly to do his work. e. None c. A web designer who uploads images of his company's products using a camera.

16.

Which of the following is a counterexample to this statement?

An individual who sprints every day is preparing for a race.
 a. Jenny who sprints every day is training for the 15k Marathon. d. Kate can not sprint due to her injuries. b. James who sprints every day is training for Mr world contest. e. None c. Drake who does not sprint evry day just completed a 25K Marathon.

17.

Which of the following is a counterexample to this statement?

If a food is red, it is a fruit.
 a. An Apple d. A tomato b. Spinach e. None c. A strawberry

18.

Which of the following is a counterexample to this statement?

If y is an odd prime, then y + 2 is also a prime.
 a. d. b. e. None c. 19.

If y is a prime numbe, which of the following must be true
 a. is odd d. y is divisible by 5 b. is not divisible by 4 e. None c. y is not divisible by 2

20.

If q is a prime number less than or equals to 10, then is prime.How many counter-examples are there to the above claim?
 a. 0 d. 3 b. 1 e. 4 c. 2

21.

If y is a prime number less than or equals to 15, then is prime.How many counter-examples are there to the above claim?
 a. 0 d. 3 b. 1 e. 4 c. 2

22.

Draw a conclusion from the given statements using the Law of Detachment

If Paul gets a 89% or above on the Science final, then Paul will pass Science.
Paul gets a 91% on the Science final.
 a. Paul will Pass Science c. A valid conclusion can not be reached. b. Paul will not pass Science d. None of the given

23.

Draw a conclusion from the given statements using the Law of Detachment

If Pandy washed the dishes today, then Penny must wash the dishes tomorrow. Pandy washed the dishes tonight.

 a. Pandy must wash the dishes tomorrow c. A valid conclusion can not be reached. b. Penny must wash the dishes tomorrow. d. None of the given

24.

Determine whether the stated conclusion is valid.

If an animal is a rat, then they like cheese.
Paul has a pet named sammy. Sammy is a rat.
Conclusion: Paul likes biscuits.
 a. Valid d. Sammy is not a rat b. Invalid e. None of the given c. A valid conclusion can not be reached.

25.

Determine whether the stated conclusion is valid.

If an integer  is even, then its square is divisible by 4.
I am thinking of a 8 digit number. The number I am thinking ends with 8.
 a. Then it's not odd. d. Then its square is divisible by 4 b. Then it's a whole number. e. None of the given c. A valid conclusion can not be reached.

26.

Determine whether the stated conclusion is valid.

If the book's binding is torn, the student will have to pay for a new one. Since Eric must pay for a new book. Hence,he claims that the binding on his book is torn. Is he right?
 a. Yes d. Not sure b. No e. None of the given c. A valid conclusion can not be reached.

27.

Which law of logic is this:

If Sally buy a dress, then she will  eat healthy.
Sally bought a dress.
Therefore,Sally will eat healthy.
 a. Law of Syllogism d. Law of Biconditional b. Law of Contrapositive e. None of the given c. Law of Detachment

28.

Which law of logic is this:

p q
q r Which law is modeled?
 a. Law of Syllogism d. Law of Biconditional b. Law of Contrapositive e. None of the given c. Law of Detachment

29.

Which law of logic is this:

p q
p Which law is modeled?
 a. Law of Syllogism d. Law of Biconditional b. Law of Contrapositive e. None of the given c. Law of Detachment

30.

Which law of reasoning is this:

If a triangle is equilateral, then all three sides are congruent.
If all the sides of a triangle are congruent, then all the three exterior angles are congruent.

Therefore, if a triangle is equilateral, then the exterior angles are congruent.

 a. Law of Syllogism d. Law of Biconditional b. Law of Contrapositive e. None of the given c. Law of Detachment

31.

Determine whether the stated conclusion is valid.

If a triangle is equilateral, then all three sides are congruent.
If all the sides of a triangle are congruent, then all the three exterior angles are congruent.

Triangle ABC is equilateral, then the exterior angles triangle ABC are congruent.

 a. Not Valid d. Might be valid b. Not Sure e. None of the given c. Valid

32.

Use the law of syllogism to draw a conclusion from the two given statements:

Statement 1: If you consistently workout, you have a good body.
Statement 2: If you have a good body, you would have more energy.
 a. You have more energy d. If you exercise consistently, then you would have more energy b. You have a good body e. None of the given c. If you do not have a good body, then you do not exercise consistently

33.

Use the Law of Detachment to draw a conclusion from the two given

Statement 1: if James prep for one hour a day, then James would do better on the test .
Statement 2: James is confident that he can do well on the test.
 a. James prep for 1 hour each day. c. If James do well on the exam,James studied for 1 hour each day. b. James do not prep for 1 hour each day. d. A valid conclusion can not be reached.

34.

Using the Law of Syllogism, which of the following completes the statement to form a valid conclusion?

If it begins to snow heavily, school will be suspended.
if school is suspended, the biology test will not be given today.

It began to snow heavily, therefore ________________.

 a. look out for the snowplows while driving to school. c. the biology test will not be given today. b. the roads will be hard to drive on. d. The school might be cancelled today.

35.

Using the Law of Syllogism, which of the following completes the statement to form a valid conclusion?

If it begins to snow heavily, school will be suspended.
if school is suspended, the biology test will not be given today.

It began to snow heavily, therefore ________________.

 a. look out for the snowplows while driving to school. c. the biology test will not be given today. b. the roads will be hard to drive on. d. The school might be cancelled today.

36.

Using the Law of Syllogism, determine whether the stated conclusion is valid.

Some dogs are poodles.
Poodles are cool.
Some dogs are cool.

 a. Valid c. might be valid. b. Not valid d. None of the given

37.

Using the Law of Syllogism, determine whether the stated conclusion is valid.

All sherbet is ice cream.
Sherbet is orange.
Conclusion: All ice cream is orange.
 a. Valid c. might be valid. b. Not valid d. None of the given

38.

Using the Law of Syllogism, determine whether the stated conclusion is valid.

All pencils are gray.
No pens are gray.

Conclusion: No pen is gray

 a. Valid c. might be valid. b. Not valid d. None of the given

39.

Using the Law of Syllogism, determine whether the stated conclusion is valid.

All Lions are brown.
No pig is a Lion.
Conclusion: No pigs are brown.
 a. Valid c. might be valid. b. Not valid d. None of the given

40.

Using the Law of Syllogism, determine whether the stated conclusion is valid.

All toys from that store are from China.
These toys are from that store.
Conclusion: Some of these toys are from China.
 a. Valid c. might be valid. b. Not valid d. None of the given

41.

Using the Law of Syllogism, determine whether the stated conclusion is valid.

If Bond dress sloppy, Bond will not look smart.
If Bond don’t look smart, Bond will loose confident.
Conclusion: If Bond dress sloppy, Bond will loose confident.

 a. Valid c. might be valid. b. Not valid d. None of the given

42.

Using the Law of Syllogism, determine whether the stated conclusion is valid.

Some People are more than 6 feet tall.
Some people who are more than 6ft tall like basketball.
All basketball fans also love football.
Conclusion: Some people who are more than 6ft tall are football fans.

 a. Valid c. might be valid. b. Not valid d. None of the given

43.

Assume that all mils are hils, some hils are jils, and some tils are rils.
Therefore it makes sense that:

 a. all mils are jils d. some jils are hils b. all hils are mils e. some mils are hils c. all tils are hils

44.

Assume that some huys are knis, all jiks are suds, and some aws are huys.
Therefore it makes sense that:
 a. some knis may also be aws d. some suds are knis b. all huys are knis e. all huys are knos c. all jiks are huys