Logical Reasoning

Which of the following is a statement?

• What is your name?

• 5 is an even number.

• Clean your room now!

• Run as fast as you can.

Which of the following represents the negation of the statement:
"All students passed the exam"?

• Some students passed the exam.

• No student passed the exam.

• Some students did not pass the exam.

• All students did not pass the exam.

If the statement "If it rains, then the ground will be wet" is true, which of the following must also be true?

• If the ground is wet, then it rained.

• If it does not rain, the ground is not wet.

• If the ground is not wet, then it did not rain.

• If it does not rain, the ground might still be wet.

Which of the following is the contrapositive of the statement:
"If you exercise, then you will be healthy"?

• If you do not exercise, then you will not be healthy.

• If you are not healthy, then you did not exercise.

• If you do not exercise, then you will be healthy.

• If you are healthy, then you exercised.

Consider the following statements:

1. If Ali studies, he will pass the exam.

2. If Ali does not pass the exam, then he did not study.

What kind of reasoning connects these two statements?

• Converse reasoning
  

• Contrapositive reasoning
  

• Inverse reasoning

• Biconditional reasoning

In a class, the following conditions are true:

1. If Sarah is in the class, then Ben is also in the class.

2. If Ali is not in the class, then Sarah is not in the class.

Which of the following must be true?

• If Ali is not in the class, then Ben is not in the class.

• If Sarah is in the class, then Ali and Ben must also be in the class.

• If Ben is in the class, then Ali must also be in the class.

• If Ali is not in the class, then Ben is in the class.

Which of the following is logically equivalent to the compound statement:
"If it is not sunny OR it is not windy, then I will stay indoors"?

• If it is sunny AND windy, then I will not stay indoors.

• If it is not windy AND not sunny, then I will stay indoors.

• If I stay indoors, then it is not sunny OR not windy.

• If I do not stay indoors, then it is sunny AND windy.

Which of the following is a universal statement?

• All students in this school study Mathematics.

• Some students in this school like sports.

• There is a student who enjoys science fiction books.

• Most students prefer online learning.

Let p and q represent the following statements:

• p: "x is a positive number."

• q: "x is a prime number."

Which of the following represents the contrapositive of the statement:

"If x is not a prime number, then x is not a positive number"?

• If x is a prime number, then x is a positive number.

• If x is a positive number, then x is a prime number.

• If x is not positive, then x is not a prime number.

• If x is a positive number, then x is not a prime number.

A survey is conducted on 50 students regarding their interest in Mathematics and Science. The results are as follows:

1. 30 students like Mathematics.

2. 25 students like Science.

3. 15 students like both Mathematics and Science.

How many students like only Science?

• 10

• 15

• 20

• 25