Reviewer_Math Logic

Which of the following statements is a proposition?

• Are you coming to the party?

• All dogs are mammals.

• Please close the door.

• What time is it?

Which of the following is NOT a proposition?

• 2 + 2 = 4

• All dogs are mammals.

• Close the door.

• The Earth orbits the Sun.

Identify the proposition in the following statements:

• If it rains tonight, then the ground will be wet.

• Close the window.

• What a beautiful day!

• How tall is that building

Which of the following statements is a compound proposition?

• The sun is shining.

• It is cold outside.

• If I eat vegetables, I will be healthy.

• Turn off the lights.

Which is a conditional statement?

• π is not an integer if and only if ππ is not in the number line.

• 2 is positive factor of 12 and 2 is a prime number.

• The set of natural numbers is infinite or all positive integers has a cardinality of 0.

• If 4 is a factor of 16, then 16 is a composite number.

Given the three propositions : p : She was enrolled in this class. q: She passed the test. r: She left the room early. What is the sentence of this symbol (∼ 𝑝) ↔ (~𝑞)?

• She was not enrolled in this class if and only if she left the room early.

• If and only if she enrolled in this class then, she pass the test.

• If she was enrolled in this class then, she did not pass the test.

• she was not enrolled in this class if and only if she did not pass the test.

Let p be “Marc is happy” and let q be “Marc is in love.” Transform this symbol in a sentence ~p → q

• If Marc is not happy, then he is in love

• It is not the case that Marc is not happy.

• Marc is not in love but he is happy.

• Marc is happy or in love.

In Conditional Truth Table p → q becomes False if

• p is true and q is false

• none of these

• both p and q are true

• both p and q are false

What is the first step in constructing a truth table?

• Perform the rules in propositional logic

• Form the table for assertion

• Construct the negation of the compound statement.

• Write the converse of the implication statement

By constructing a truth table, what is the truth value of the statement

(p ∧ r) → ∼ q, if p is T, q is T and r is T?

• True

• False