Free Printable MIDTERM: SET THEORY AND MATH LOGIC

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MIDTERM: SET THEORY AND MATH LOGIC

Total questions: 50

Worksheet time: 53mins

Name

Class

Date

Which of the following statements are true for the Venn diagram shown?

A ∩ B = ⊘

A ⋃ B = ⊘

A ⋃ B = A

A ⋂ B = A

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∩ B?

{3, 5, 7}

{2, 3, 5, 7}

{2, 3, 5, 7, 9}

{1, 2, 3, 5, 7, 9}

The Universal Set = { -4, 3, -2, -1, 0, 1, 2, 3 ,4} and A = {0}.
What is the complement of A?

{-4, -3, -2, -1, 0, 1, 2, 3}

{-3, -2, -1, 1, 2, 3}

{-4, -3, -2, -1, 1, 2, 3, 4}

{-4, -3, -2, -1, 1, 2, 3}

From the above Venn diagram, what is the set S ∩ T?

{casey, drew, jade, glen}

{alex, casey, drew,hunter}

{casey, drew}

{drew, jade}

From the above Venn diagram, what is the set (S ∪ T) ∩ V?

{casey, drew, jade, glen}

{alex, glen, hunter, jade}

{casey, drew, glen}

{drew, jade}

From the above Venn diagram, what is the set S' ? Look at ALL of the Universal set called "U."

{casey, drew}

{blair, francis, glen, jade}

{blair, erin, francis, ira}

{jade, glen, blair, erin, francis, ira}

How many students do not ski or ice skate?

How many students do not snowboard?

What does the shaded region of the Venn diagram represent?

P or S

Only P or S

P and S

Only P and S

10.

What statement does the shaded region represent?

A and B and C

A or B and C

B and C

A or C

11.

What statement does the shaded region represent?

A or B and C

Not C

A or B

B and C or A

12.

What statement does the shaded region represent?

A ∩ B ∩ C

A ∪ B ∩ C

B ∩ C

A ∪ C

13.

Which of the following represents the shaded region?

(A ⋃ B)'

(A ∩ B)'

14.

It is an operation on sets that contains elements belong to set A, but do not belong to set B.

Complement of a Set

Difference of Two Sets

Intersection of Sets

Union Sets

15.

It is an operation on sets that contains elements belong to set A, but do not belong to set B.

Complement of a Set

Difference of Two Sets

Intersection of Sets

Union Sets

16.

Which relation is NOT a function?

{(1,-5), (3,1), (-5,4), (4,-2)}

{(2,7), (3,7), (4,7), (5,8)}

{(1,-5), (-1,6), (1,5), (6,-3)}

{(3,-2), (5,-6), (7,7), (8,8)}

17.

All of the x values or inputs are called what?

Domain

Range

Relation

Function

18.

All of the y values or outputs are called what?

Domain

Range

Relation

Function

19.

Which of the following is not a function?

{(0,1), (1,2), (2,3), (3,4)}

{(0,2), (1,3), (4,3), (1,2)}

{(1,3), (4,2), (2,0), (3,4)}

{(1,2), (2,2), (3,2), (4,2)}

20.

Is the relation a function? Why.

Yes, because the x-value 11 has two y-values pair with it.

Yes, because each x-value has only one y-value paired with it.

No, because the x-value 11 has two y-values pair with it.

No, because each x-value has only one y-value paired with it.

21.

List the ordered pairs

(1,3), (2,6), (3,9), (4,12)

(3,1), (6,2), (9,3), (12,4)

Input and Output

Output and Input

22.

Determine if the relation is a function

Not a function, each input has more than one output

Yes it is a function, because each input has exactly on output

Not a function, input is equal to output

Yes it is a function, -1/2 is a fraction of 2

23.

For the given sets A and B, which statement is true?

A ⊂ B

B ⊂ A

A = B

A^'= B

24.

Given that
set V = { m, n, o, p },
find the number of subsets V.

25.

P' ∪ R' ∪ Q

( P ∪ R )' ∩ Q

Q ∩ ( P ∩ R )'

R' ∩ Q' ∩ P'

26.

Find n(A) when

A = {14, 16, 18, 20, 22, 24}

even numbers

27.

P = {0, 1, 2, 3, 4}, Q = {4, 6, 8}

R = {6, 12, 18} Then what is (P ∩ Q) ∪ (Q ∩ R)?

{4}

{4, 6}

{4, 6, 8}

{1, 2, 3, 4, 6, 8}

28.

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∪ B?

{3, 5, 7}

{2, 3, 5, 7}

{2, 3, 5, 7, 9}

{1, 2, 3, 5, 7, 9}

29.

The Universal Set = { -4, -3, -2, -1, 0, 1, 2, 3 ,4} and A = {0}.

What is the complement of A?

{-4, -3, -2, -1, 0, 1, 2, 3}

{-3, -2, -1, 1, 2, 3}

{-4, -3, -2, -1, 1, 2, 3, 4}

{-4, -3, -2, -1, 1, 2, 3}

30.

Which of the following is a finite set?

J = {x ∈ N | x is a factor of 35}

U = {x ∈ N|x is a multiple of 15}

D = {x ∈N|x is a divisible by 7}

Y= {x ∈ Q|x is a factor of 3}

31.

Which set is equivalent to

B = {x ∈ N| x is a multiple of 5 between 5 &19}

L= {5,10,15}

M= {shake, rattle, roll}

A= {x ∈ N| 5<x<19}

O= {x | x is a vowel in the word positivity}

32.

Which of the following is the symbol for null set?

∅

$\subset$

$\in$

$\not\subset$

33.

How do you write "the complement of A"?

n(A)

(A)

$\forall$

34.

What is the Domain?

{-3, -1, 1, 3, 5, 7, 9}

{-3, -2, -1, 0, 1, 2, 3}

-3 ≤ x ≤ 3

-3 ≤ x ≤ 9

35.

What is the domain?

{-4, -1, 0, 2, 7}

{-5, -4, -1, 0, 1, 2, 4, 7}

{-5, 0, 1, 2, 4}

{5}

36.

Which set of ordered pairs is not a function?

{ (0,0), (1,1), (2,2) }

{ (3,5), (5,3), (4,4) }

{ (0,0), (1,0), (0,-1) }

{ (3,0), (1,1), (5,-2) }

37.

Which of the following is not a function?

one – to – one relation

one – to – many relation

many – to – one relation

A and C

38.

Which of the following statements is incorrect?

Every set is a subset of itself.

An empty set is always a subset of every set

The number of subsets of a given set is 2ⁿ where n denotes number of elements of the set.

A relation is a function in which no two ordered pairs have the same 1^st coordinate and different 2^nd coordinate.

39.

Let R be a relation in the set {1,2,3,4} given by R={(1,2), (2,2), (1,1), (4,4), (1,3), (3 ,3), (3,2)} Then R is

a) R is Reflexive and symmetric but not transitive

a) R is Reflexive and transitive but not symmetric

a) R is symmetric and transitive but not reflexive

a) R is an equivalence relation

40.

Let R be the relation in the set N given by R = {(a ,b) : a = b – 2 , b > 6}, Then

(2 , 4) $\in$ R

(3 , 8) undefined R

(6 , 8) undefined R

(8 , 7) undefined R

41.

Let R be a relation on set of lines as L₁ R L₂ if L₁ is perpendicular to L₂. Then

R is Reflexive

R is Symmetric

R is Transitive

R is equivalence relation

42.

Given a set A = {a , b, c} Then the identity relation is the set

{(a ,c) , (a ,b)}

{(a , a) , (b ,b) , (c ,c)}

{(a ,a), (b , a), (c , a)}

{(a , a) , (b ,b) , (c ,c), (a ,c)}

43.

If A= {10,20,30,40},B={20,40,60} and C = {10,20,40,60,80}, find A Ո B Ո C

{20,40}

{20,40,60}

{10,20,30,40,50,60,80}

{10,20,30,...}

44.

Which of the following sets is an infinite set?

A={9,7,5,3,1}

B={2,4,6,8,...}

C={x|x=positive odd integer less than 10}

C={x|x=negative even integer less than 10}

45.

Given that A={@,#,$,%,^,&}, what is n(A)?

infinite

46.

It is given that the universal set, ξ = {x : x is an integer, $1\le x\le10$ }, set P = {x : x is an odd number} and
set Q = {x : x is a prime number}. List the elements of $P\cap Q$ .

{1, 3, 5, 7, 9}

{2, 3, 5, 7}

{3, 5, 7}

{1,2,3, 5, 7,9}

47.

Which of the following operations on sets describe the given Venn diagram?

$A'-B'$

$\left(A\cup B\right)'$

$A'\cup B'$

\left(A\cap B\right)'

48.

$\left(A\cap B\right)'$

{1,2,3,4,5,7,8}

{1,3,4,8}

{1,3,4,5,7,8}

{5,7}

49.

$\left(A\cup B\right)'$

{1,2,3,4,5,7,8}

{1,3,4,8}

{1,3,4,5,7,8}

{5,7}

50.

X ∩ Y ∩ Z

{ }

{Phillip}

{Billy, Phillip, Bryan, Perez}

{Billy, Perez, Bryan}

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MIDTERM: SET THEORY AND MATH LOGIC

Total questions: 50

Worksheet time: 53mins

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