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WorksheetsY1 Workshop math quiz
Total questions: 20
Worksheet time: 15mins
Definition: A real interval that contains no minimum, which is a real number smaller than all
other elements in the interval
Left-open interval
Right-open interval
Open interval
Closed interval
The empty set, [a, a), ∀a∈ℝ, and the singleton set, [a, a], ∀a∈ℝ, are considered
Right-open interval
Half-open interval
Right-closed interval
Left-closed intervals
A real interval, for which there exists one real number smaller than all
elements in the interval and there exist another real number larger than all elements in the
interval
Empty interval
Degenerate interval
Proper interval
Bounded interval
If the real interval is degenerate, then
its diameter is ∞
its diameter is 0
its diameter is undefined
Definition: a function, idX: X →X, which always produces a value equal to its argument
Invertible function
Inverse function
Identity function
Involutory function
The interval, [–∞, 13], is a subset of the set of the extended real numbers [–∞, ∞]
True
False
Aleph-null is a symbol denoting the cardinality of the set of natural numbers. It is denoted with אo. If |A|<אo , then the set, A, is ?
an infinite set
an uncountably infinite set
a countably infinite set
a finite set
Every proper subset has a cardinality, which
is less than the cardinality of the set
True
False
A theorem stating that a surjective function from any set to its powerset does not
exist, implying that the cardinality of any set is less than the cardinality of its powerset
Cantor theorem
Schroder-Bernstein theorem
Bayes’ theorem
Russell’s paradox
Select the best claim:
ZFC stands for “Zermelo-Fraenkel set theory with the axiom of choice”
GCH stands for “generalized continuum hypothesis”
ZF stands for “Zermelo-Fraenkel set theory without the axiom of choice”
The vertical
line test is a visual method to determine that a plotted one-dimensional subspace is a graph of a
function or not.
True
False
If the sample space of an experiment contains exactly one outcome,
then the experiment is called
Random experiment
Composed experiment
Trial
Deterministic experiment
The Euler-Venn diagram illustrates the term
continuum of events
complement of an event
conditional event
complementary group of events
The complement of the union of the events, A and B, equals the intersection
of the complements of А and B:
A∪B=A ∩B
First De Morgan’s law
Second De Morgan’s law
Hilbert’s paradox of the Grand Hotel
Cantor’s paradox
Select the best claim:
The closure of the real interval (70, 70) is [70, 70]
The closure of the real interval (15, ∞) is [15, ∞)
The closure of the real interval (–∞, 15] is (–∞, 15)
None of the above
Select the best claim:
If a function maps real numbers to real numbers, then it is a real function
Any real function is a real-valued function of a real variable
The function f: N → R is a real function
All of the above
Select the best claim:
The inclusion function, ι: A →B is a special case of the identity function, id A : A →A
The, ι: A →B is the inclusion functions, then A ⊇ B
The, ι: A →B is the inclusion functions, then A ⊆B
None of the above
Select the best claim:
If a function is involutory, then it is invertible
If a function is invertible involutory, then it is involutory
If a function is involutory, then the domain should be a proper subset of the codomain
All of the above
Given the set, S= (3, 12]∪ (14, 16]∪ {2, 13, 28}.
Select the best claim:
The real 12 is not an internal point of S
The real 13 is not an internal point of S
The real 3 is not an internal point of S
All of the above
The set Y is a subset of ℝ.
Select the best claim:
The Hausdorff’s border of Y contains all boundary points of Y
Hausdorff’s border of Y may not contain an interior point of Y
Hausdorff’s border of Y may contain a point that does not belong to Y
None of the above
