Discrete Mathematics Prelim Exam

Which of the following is a proposition?

• What a beautiful day!

• Please close the door.

• The sun rises in the east.

• How are you today?

What is the negation of the proposition "It is raining"?

• It is not raining.

• It is always raining.

• It is raining heavily.

• Sometimes it rains.

If p is "I study" and q is "I pass the exam," what is the symbolic form of "If I study, then I pass the exam"?

• p∨q

• p→q

• p∧q

• q→p

Which logical operator represents a conjunction?

• ∨

• ∧

• →

• ↔

What is the truth value of the conjunction "2 is even and 3 is odd"?

• True

• False

• Sometimes true

• Cannot be determined

What is the converse of the implication "If it is raining, then the ground is wet"?

• If the ground is wet, then it is raining.

• If it is not raining, then the ground is not wet.

• If the ground is not wet, then it is not raining.

• The ground is wet if and only if it is raining.

What is the contrapositive of the statement "If today is Monday, then tomorrow is Tuesday"?

• If tomorrow is Tuesday, then today is Monday.

• If tomorrow is not Tuesday, then today is not Monday.

• If today is not Monday, then tomorrow is Tuesday.

• Today is Monday if and only if tomorrow is Tuesday.

What is the result of the disjunction "5 is even or 10 is even"?

• True

• False

• Cannot be determined

• Neither true nor false

What is the truth value of the biconditional statement "4 is even if and only if 9 is odd"?

• True

• False

• Cannot be determined

• Sometimes true

What is the inverse of the statement "If a number is divisible by 4, then it is even"?

• If a number is even, then it is divisible by 4.

• If a number is not even, then it is not divisible by 4.

• If a number is not divisible by 4, then it is not even.

• A number is divisible by 4 if and only if it is even.