Level 2 Logical Reasoning

If the statement "If it rains, then the ground will be wet" is true, which of the following is a valid logical conclusion?

• If the ground is wet, then it rained.

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

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

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

The statement "Ali is a student AND Ali likes Mathematics" is true. If Ali does not like Mathematics, what can you conclude?

• Ali is not a student.

• The statement is false.

• Ali likes Mathematics.

• Ali is a student.

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

• No student passed the exam.

• Some students did not pass the exam.

• Some students passed the exam.

• All students did not pass the exam.

Given the statements:

• p: "I study hard."

• q: "I pass the exam."

• Which of the following is the converse of the statement "If I study hard, then I pass the exam"?

• If I do not study hard, then I do not pass the exam.

• If I pass the exam, then I study hard.

• If I do not pass the exam, then I do not study hard.

• If I study hard, then I pass the exam.

Which of the following is not a compound statement?

• "Kuala Lumpur is the capital city of Malaysia."

• "The sun rises in the east AND sets in the west."

• "Either Ali plays football OR he plays badminton."

• "If it rains, then I will stay at home."

If the statement "If x > 2, then x² > 4" is true, which of the following is a counterexample?

• x = 3

• x = -3

• x = 2

• x = -2

If the truth values of statements p and q are as follows:

• p: True

• q: False

What is the truth value of the compound statement "p AND q"?

• True

• False
  

• True only if p is false

• none

A teacher said, "If a student completes their homework, they will get extra marks." Which of the following statements represents the contrapositive?

• If a student does not complete their homework, they will not get extra marks.

• If a student does not complete their homework, they might not get extra marks.

• If a student gets extra marks, they completed their homework.

• If a student does not get extra marks, they did not complete their homework.

Which of the following represents a universal statement?

• At least one student submitted the assignment.

• No student in the class failed the test.

• All members of the club attended the meeting.

• Some people enjoy solving mathematical problems.

Let p and q be the following statements:

• p: "x is a positive number."

• q: "x is greater than 10."

Which of the following represents the compound statement "p OR q"?

• x is a positive number or x is greater than 10.

• x is not a positive number or x is greater than 10.

• If x is a positive number, then x is greater than 10.

• x is both a positive number and greater than 10.