Self Exercise Topic 3-Universal Quantifiers

Which symbol represents the universal quantifier in logic?

• ∃

• ∈

• ∧

• ∀

What does the universal quantifier (∀) mean in logic?

• Expresses that a statement is true for every element in a set or domain.

• Expresses that a statement is true for no elements in a set or domain.

• Expresses that a statement is true for only one element in a set or domain.

• Expresses that a statement is true for some elements in a set or domain.

In a statement with a universal quantifier, if the quantifier is false, what can we conclude about the statement?

• The statement is true.

• The quantifier is true.

• The quantifier is unknown.

• The statement is false.

True or False: The universal quantifier (∀) is used to assert that a statement is true for every element in a set.

• True

• Only for numbers

• Sometimes

• False

What is the negation of the statement 'For every natural number n, n is greater than 0'?

• There exists a natural number n such that n is equal to 0

• There exists a natural number n such that n is not greater than 0

• There exists a natural number n such that n is less than 0

• For every natural number n, n is less than or equal to 0

In a proof using universal quantifiers, what is the first step?

• Start by proving the statement for all elements in the domain.

• Assume the statement is true for an arbitrary element in the domain.

• Assume the statement is false for an arbitrary element in the domain.

• Skip the first step and directly prove the statement for a specific element in the domain.

What is the truth value of the statement 'For every real number x, x squared is greater than or equal to 0'?

• negative

• true

• undefined

• false

What is the truth value of the statement 'For every integer n, n is divisible by 2'?

• not sure

• false

• true

• sometimes true

What is the negation of the statement 'For every positive integer n, n is prime'?

• There exists a positive integer n that is prime

• For every positive integer n, n is not prime

• There exists a positive integer n that is prime and not prime

• There exists a positive integer n that is not prime

What is the truth value of the statement 'For every real number x, x plus 0 equals x'?

• false

• undefined

• x plus 0 is not defined

• true