Mathematical Logic and Quantifiers Quiz

Which of the following is the correct symbol for 'for all'?

The statement '∃ x, x is a prime number' is true.

What does the symbol '⇒' represent in mathematical logic?

The statement 'If it is raining, then the ground is wet' can be written in symbolic form as P ______ Q.

Match the following symbols with their corresponding meanings:

Which of the following statements is true regarding the Euler Diagram representing P ⇒ Q?

The statement '∀ x, x² ≥ 0' means that all real numbers have negative squares.

What is the most relevant quantifier to add to the statement 'm is an even number' to make it true as often as possible?

What can be concluded about the product of any three consecutive numbers?

The sum of any four consecutive numbers is odd.

What is the remainder when $a^k$ is divided by 5 if $a$ is not divisible by 5?

The expression $(k^3 - k)(2k^2 + 5k - 3)$ is divisible by _____ without using induction.

Match the following statements with their proofs:

What happens to the inequality sign when multiplying both sides by a positive number?

Dividing both sides of an inequality by a negative number will keep the sign the same.

What should you do when performing an operation that matches a function that is not monotonic?

When taking the tangent of both sides of an inequality, we need _______ to determine the behavior.

Match the operation with its effect on the inequality sign:

For which operation will the sign definitely change?

Taking the reciprocal of both sides of an inequality never requires more information.

If a > b > 0, what can we conclude about 2^{-a} compared to 2^{-b}?

What is a suitable approach for proving a statement is false?

Proof by cases requires each case to support the statement.

What is the contradiction when proving that there cannot be a Pythagorean triad where all numbers are odd?

The sum of the squares of two consecutive even numbers is divisible by ____ but not by ____.

For which of the following statements is a real number solution found?

There exists a real number x such that x^2 + 2x + 5 < 0.

What is the general form to express two consecutive even numbers using an integer k?

Match the proof techniques with their descriptions:

What is the negation of the statement '𝑥 ≥ 4'?

The statement 'If 𝑥 is composite, then 2𝑥 + 1 is prime' has the same contrapositive as 'If 2𝑥 + 1 is not prime, then 𝑥 is not composite.'

What is the concept of negation in mathematics?

The negation of the statement '𝑥 < 5' is __________.

Match the inequality with its negation:

Which of the following statements is NOT an example of negation?

The contrapositive of the statement 'If 𝑥 is even, then 𝑥^2 is even' is 'If 𝑥^2 is not even, then 𝑥 is not even.'

What does proof by contradiction entail?

Which of the following statements about multiples of 3 and multiples of 9 is true?

The sum of any four consecutive integers is always odd.

What is the product of any two odd integers?

If m is an even integer, then 𝑚2 is ___.

Match the following properties with their corresponding outcomes:

Which of the following correctly states a property regarding multiples of 16?

The product of any two even integers is always odd.

What is the result of adding two odd integers?

The expression for the sum of two consecutive integers k and (k + 1) is ___.

What can be concluded about the sum of an odd and an even integer?