Mathematical Reasoning and Proof

Description: Mathematical Reasoning and Proof Quiz
Number of Questions: 15
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Tags: mathematical reasoning proofs logic deductive reasoning
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Which of the following statements is a valid deduction from the premises "All dogs are mammals" and "All mammals are animals"?

  1. All dogs are animals.

  2. All animals are dogs.

  3. All mammals are dogs.

  4. All animals are mammals.


Correct Option: A
Explanation:

The correct answer is "All dogs are animals." This is a valid deduction because the premises establish that all dogs are mammals and all mammals are animals. Therefore, it can be logically concluded that all dogs are animals.

Which of the following statements is a valid deduction from the premises "If it is raining, then the ground is wet" and "The ground is wet"?

  1. It is raining.

  2. It is not raining.

  3. The ground is dry.

  4. The sky is blue.


Correct Option: A
Explanation:

The correct answer is "It is raining." This is a valid deduction because the premises establish that if it is raining, then the ground is wet, and the ground is wet. Therefore, it can be logically concluded that it is raining.

Which of the following statements is a valid deduction from the premises "All prime numbers are odd" and "7 is a prime number"?

  1. 7 is odd.

  2. 7 is even.

  3. All odd numbers are prime.

  4. All even numbers are prime.


Correct Option: A
Explanation:

The correct answer is "7 is odd." This is a valid deduction because the premises establish that all prime numbers are odd and 7 is a prime number. Therefore, it can be logically concluded that 7 is odd.

Which of the following statements is a valid deduction from the premises "All squares have four sides" and "This shape has four sides"?

  1. This shape is a square.

  2. This shape is not a square.

  3. This shape has four corners.

  4. This shape is a rectangle.


Correct Option: A
Explanation:

The correct answer is "This shape is a square." This is a valid deduction because the premises establish that all squares have four sides and this shape has four sides. Therefore, it can be logically concluded that this shape is a square.

Which of the following statements is a valid deduction from the premises "If I study hard, then I will pass the exam" and "I studied hard"?

  1. I will pass the exam.

  2. I will not pass the exam.

  3. I did not study hard.

  4. I am not sure if I will pass the exam.


Correct Option: A
Explanation:

The correct answer is "I will pass the exam." This is a valid deduction because the premises establish that if I study hard, then I will pass the exam, and I studied hard. Therefore, it can be logically concluded that I will pass the exam.

Which of the following statements is a valid deduction from the premises "All birds have wings" and "Penguins are birds"?

  1. Penguins have wings.

  2. Penguins do not have wings.

  3. All birds are penguins.

  4. All penguins are birds.


Correct Option: A
Explanation:

The correct answer is "Penguins have wings." This is a valid deduction because the premises establish that all birds have wings and penguins are birds. Therefore, it can be logically concluded that penguins have wings.

Which of the following statements is a valid deduction from the premises "If it is sunny, then I will go to the beach" and "It is not sunny"?

  1. I will go to the beach.

  2. I will not go to the beach.

  3. It is sunny.

  4. It is not sunny.


Correct Option: B
Explanation:

The correct answer is "I will not go to the beach." This is a valid deduction because the premises establish that if it is sunny, then I will go to the beach, and it is not sunny. Therefore, it can be logically concluded that I will not go to the beach.

Which of the following statements is a valid deduction from the premises "All roses are red" and "This flower is red"?

  1. This flower is a rose.

  2. This flower is not a rose.

  3. All red flowers are roses.

  4. All roses are red flowers.


Correct Option: A
Explanation:

The correct answer is "This flower is a rose." This is a valid deduction because the premises establish that all roses are red and this flower is red. Therefore, it can be logically concluded that this flower is a rose.

Which of the following statements is a valid deduction from the premises "If I eat chocolate, then I will get a headache" and "I did not get a headache"?

  1. I ate chocolate.

  2. I did not eat chocolate.

  3. Chocolate always gives me a headache.

  4. Chocolate never gives me a headache.


Correct Option: B
Explanation:

The correct answer is "I did not eat chocolate." This is a valid deduction because the premises establish that if I eat chocolate, then I will get a headache, and I did not get a headache. Therefore, it can be logically concluded that I did not eat chocolate.

Which of the following statements is a valid deduction from the premises "All triangles have three sides" and "This shape has three sides"?

  1. This shape is a triangle.

  2. This shape is not a triangle.

  3. All shapes with three sides are triangles.

  4. All triangles are shapes with three sides.


Correct Option: A
Explanation:

The correct answer is "This shape is a triangle." This is a valid deduction because the premises establish that all triangles have three sides and this shape has three sides. Therefore, it can be logically concluded that this shape is a triangle.

Which of the following statements is a valid deduction from the premises "If I exercise regularly, then I will be healthy" and "I am healthy"?

  1. I exercised regularly.

  2. I did not exercise regularly.

  3. Exercise always makes me healthy.

  4. Exercise never makes me healthy.


Correct Option: A
Explanation:

The correct answer is "I exercised regularly." This is a valid deduction because the premises establish that if I exercise regularly, then I will be healthy, and I am healthy. Therefore, it can be logically concluded that I exercised regularly.

Which of the following statements is a valid deduction from the premises "All cats are mammals" and "This animal is a cat"?

  1. This animal is a mammal.

  2. This animal is not a mammal.

  3. All mammals are cats.

  4. All cats are animals.


Correct Option: A
Explanation:

The correct answer is "This animal is a mammal." This is a valid deduction because the premises establish that all cats are mammals and this animal is a cat. Therefore, it can be logically concluded that this animal is a mammal.

Which of the following statements is a valid deduction from the premises "If I drink coffee, then I will stay awake" and "I stayed awake"?

  1. I drank coffee.

  2. I did not drink coffee.

  3. Coffee always keeps me awake.

  4. Coffee never keeps me awake.


Correct Option: A
Explanation:

The correct answer is "I drank coffee." This is a valid deduction because the premises establish that if I drink coffee, then I will stay awake, and I stayed awake. Therefore, it can be logically concluded that I drank coffee.

Which of the following statements is a valid deduction from the premises "All fruits contain vitamins" and "This food contains vitamins"?

  1. This food is a fruit.

  2. This food is not a fruit.

  3. All foods that contain vitamins are fruits.

  4. All fruits are foods that contain vitamins.


Correct Option: A
Explanation:

The correct answer is "This food is a fruit." This is a valid deduction because the premises establish that all fruits contain vitamins and this food contains vitamins. Therefore, it can be logically concluded that this food is a fruit.

Which of the following statements is a valid deduction from the premises "If I eat too much sugar, then I will get a stomachache" and "I did not get a stomachache"?

  1. I ate too much sugar.

  2. I did not eat too much sugar.

  3. Sugar always gives me a stomachache.

  4. Sugar never gives me a stomachache.


Correct Option: B
Explanation:

The correct answer is "I did not eat too much sugar." This is a valid deduction because the premises establish that if I eat too much sugar, then I will get a stomachache, and I did not get a stomachache. Therefore, it can be logically concluded that I did not eat too much sugar.

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