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WorksheetsSets and Set Operations Quiz
Total questions: 62
Worksheet time: 34mins
Which of the following is a well-defined set?
The set of tall students
The set of beautiful flowers
The set of vowels in the English alphabet
The set of interesting books
If A={1,2,3}, which of the following is an element of A?
0
2
4
5
Which notation means “x is an element of set A”?
x⊂A
x∈A
x∪A
x∩A
If A={a,b,c} and B={b,c,d}, what is A∩B?
{a,d}
{b,c}
{a,b,c,d}
{b}
What is the union of A={1,2} and B={2,3}?
{2}
{1,2,3}
{1,3}
{1,2}
If A={1,2,3} and B={3,4}, what is A−B?
{3}
{4}
{1,2}
{1,2,3,4}
Which symbol represents the empty set?
{}
0
∅
1
If a set has no elements, it is called a
finite set
null set
universal set
equal set
If A⊂B, then
A has more elements than B
A has exactly the same elements as B
Every element of A is in B
A and B are disjoint
Which of the following is a subset of {1,2}?
{3}
{1}
{1,2,3}
{2,3}
The number of elements in a set is called
union
cardinality
subset
complement
What is the cardinality of {a,b,c,d}?
3
4
5
6
If the universal set is U={1,2,3,4} and A={1,3}, what is A′?
{1,3}
{2,4}
{1,2}
∅
Which operation gives elements common to two sets?
Union
Difference
Complement
Intersection
If A∩B=∅, then A and B are
equal
subsets
disjoint
universal
What is the Cartesian product A×B of A={1,2} and B={a}?
{(a,1),(a,2)}
{(1,a),(2,a)}
{1,2,a}
{(1,2)}
How many elements are in A×B if |A|=2 and |B|=3?
5
6
9
12
The power set of a set is
the set of all elements
the set itself
the set of all subsets
the universal set
How many elements are in the power set of a set with 3 elements?
3
6
8
9
Which of the following is TRUE about power sets?
They have fewer elements than the original set
They contain only proper subsets
They contain the empty set
They exclude the original set
If A={x∣x<5,x∈N}, which is A?
{0,1,2,3,4}
{1,2,3,4}
{2,3,4}
{1,3,5}
Which set operation combines all elements without repetition?
Intersection
Union
Complement
Difference
If A=B, then
A⊂B only
B⊂A only
Both A ⊆ B and B ⊆ A
A and B are disjoint
Which of the following is NOT a subset of {a,b}?
∅
{a}
{b}
{a,b,c}
The complement of the universal set is
the universal set
a subset
the empty set
undefined
Which operation removes common elements?
Union
Difference
Intersection
Complement
If A=∅, then |A|=
1
0
undefined
infinite
If A∩B=A, then
A ⊆ B
B ⊆ A
A = ∅
A and B are disjoint
Which of the following is a finite set?
Natural numbers
Integers
Letters in the word “SCHOOL”
Real numbers
The universal set contains
no elements
all elements under consideration
only subsets
common elements only
If |A|=4, how many subsets does A have?
The universal set contains
no elements
all elements under consideration
only subsets
common elements only
If |A|=4, how many subsets does A have?
8
12
16
20
Which of the following best describes a subset?
A set with more elements
A set with common elements
A set whose elements all belong to another set
A set with no elements
Which operation results in ordered pairs?
Union
Intersection
Cartesian product
Power set
If A={1,2}, which is NOT in P(A)?
∅
{1}
{2}
{1,2,3}
The difference A−B means
elements in both A and B
elements in A only
elements in B only
elements in neither
Which of the following is a proposition?
Close the door.
What time is it?
2 + 3 = 5
x + 2 = 7
A proposition is
a question
a command
a statement that is either true or false
an opinion
“x is greater than 5” is
a true proposition
a false proposition
not a proposition
a tautology
Which is a TRUE proposition?
4 is an odd number
5 + 2 = 8
The sun rises in the east
9 < 3
The negation of “It is raining” is
It is raining heavily
It is not raining
It might rain
Rain is falling
The symbol for negation is
∧
∨
¬
→
A conjunction uses the word
or
if
and
not
The conjunction p∧q is true when
p is true
q is true
both p and q are true
both p and q are false
The symbol ∨ represents
and
or
if
not
A disjunction is false when
both statements are true
one is true
both are false
one is false
An implication is written as
p∧q
p∨q
p→q
p↔q
The statement “If it rains, then the ground is wet” is an example of
conjunction
disjunction
implication
biconditional
An implication is false only when
p is false and q is false
p is false and q is true
p is true and q is false
p is true and q is true
The biconditional is written as
p→q
p∧q
p↔q
¬p
A biconditional is true when
p and q have different truth values
p and q are both false or both true
p is true only
q is true only
A tautology is a statement that is
always false
sometimes true
always true
undecidable
Which is an example of a tautology?
p ∧ ¬p
p ∨ ¬p
p → q
p ∧ q
A contradiction is
always true
sometimes true
always false
undefined
Which logical operator uses “if and only if”?
Conjunction
Disjunction
Implication
Biconditional
In a truth table, how many rows are needed for two variables?
2
3
4
8
Which logical operator gives TRUE when at least one statement is true?
AND
OR
NOT
IF
The statement ¬(p ∨ q) is equivalent to
¬p ∨ ¬q
¬p ∧ ¬q
p ∧ q
p ∨ q
Which is NOT a logical connective?
and
or
not
equal
Which truth value does ¬p have if p is false?
True
False
Both
Neither
Truth tables are used to
count elements
define sets
determine truth values of compound statements
find subsets
