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WorksheetsCIT 201
Total questions: 80
Worksheet time: 39mins
If A = {1,2,3} and B = {2,3,4}, what is A∪B?
{2,3}
{1,2,3}
{1,2,3,4}
{4}
What is the cardinality of the power set of {a,b,c}?
3
6
8
16
Which of the following is not a property of equivalence relations?
Reflexive
Symmetric
Antisymmetric
Transitive
If f (x) = 2x + 1, what is f − 1 (y)?
(y−1)/2
2y+1
y−1
2x−1
What is the result of A∖B if A = {1,2,3} and B = {2,4}?
{1,3}
{2,4}
{1,2}
{4}
Convert the binary number 1101 into decimal.
13
14
15
16
Which of the following is equivalent to 11012 + 10112?
10110
10101
11000
10001
What is the hexadecimal equivalent of 1111101?
7D
5F
3E
1A
Which number system is base-8?
Binary
Octal
Decimal
Hexadecimal
What is the 2’s complement of 1011?
0101
1101
0011
1010
Which logic gate outputs true only when all its inputs are true?
AND
OR
XOR
NOT
What is the simplified form of the Boolean expression A⋅(A + B)?
AB
A+B
A
B
Which of the following is true for De Morgan's laws?
¬(A∨B)=¬A∧¬B
¬(A∧B)=¬A∨¬B
Both a and b
Neither a nor b
If a circuit has inputs A = 1, B = 0, what is the output of A ⊕ B?
0
1
Undefined
2
What is the result of A⋅¬A?
1
0
A
¬A
How many cells are in a 3-variable Karnaugh map?
4
6
8
16
Which term corresponds to a don’t-care condition in a K-map?
0
1
X
Y
Simplify the following using a Karnaugh map: ABC + A'BC.
BC
AB+BC
A+BC
ABC
Which of the following is true for a 4-variable K-map?
It has 16 cells.
It can group up to 4 adjacent cells for simplification.
Both a and b.
None of the above.
What is the output of a combinational circuit with inputs A = 1, B = 1, C = 0 using F = A ⋅ B + C?
0
1
Undefined
2
How many ways can 4 people sit in a row?
24
16
12
32
In how many ways can a committee of 3 be chosen from a group of 10 people?
120
720
30
10
What is the value of P(5,3)?
10
60
120
20
What is the value of P(5,3)?
10
60
120
20
Which principle is used when solving: "How many ways can a pair of shoes be matched if there are 4 shoes"?
Addition principle
Multiplication principle
Pigeonhole principle
Permutations
Using the pigeonhole principle, how many students must be in a class to guarantee that at least two share the same birth month?
11
12
13
24
What is the probability of flipping two heads with two fair coins?
1/4
1/3
1/2
1/8
What is the probability of rolling an even number on a fair 6-sided die?
1/2
1/3
1/6
2/3
A card is drawn from a standard deck. What is the probability of drawing a heart?
1/2
1/3
1/4
1/6
If events A and B are independent, which of the following is true?
P(A∩B)=P(A)+P(B)
P(A∩B)=P(A)⋅P(B)
P(A∩B)=P(A)
P(A∩B)=P(B)
What is the conditional probability P(A|B) if P(A∩B)=0.2 and P(B)=0.5?
0.2
0.4
0.6
0.8
Which of the following is a transitive relation?
{(a,b),(b,c),(a,c)}
{(a,b),(b,c),(c,a)}
{(a,a),(b,b),(c,c)}
None of the above
A relation R is reflexive if...
∀a,(a,b)∈R
∀a,(a,a)∈R
∀a,(b,a)∈R
∀b,(a,b)∈R
How can a relation be represented?
As a graph
As a matrix
As a set of ordered pairs
All of the above
Which of the following is an equivalence relation?
R={(1,1),(2,2),(1,2)}
R={(a,b),(b,c),(a,c)}
R={(x,x),(y,y),(z,z)}
None of the above
If A={1,2,3}, how many binary relations can be defined on A?
8
16
64
512
Which of the following is not a logical equivalence?
P∨Q≡Q∨P
P∧(Q∨R)≡(P∧Q)∨(P∧R)
P→Q≡¬P∨Q
P∧Q≡P∨Q
What is the converse of the statement "If it rains, then I will bring an umbrella"?
If I will bring an umbrella, then it rains.
If it does not rain, I will not bring an umbrella.
If I will not bring an umbrella, then it does not rain.
If I bring an umbrella, then it rains.
Which is logically equivalent to (P→Q)∧(Q→R)?
P→R
P∧R
P∨R
R→P
Which of the following arguments is valid?
P→Q,Q→R,∴P→R
P∧Q,Q→R
If (P→Q)∧(Q→R)?
P→R
P∧R
P∨R
R→P
Which of the following arguments is valid?
P→Q, Q→R, ∴P→R
P∧Q, Q→R, ∴P∨R
P∨Q, ¬Q, ∴P∨R
None of the above
What is the result of applying the rule of universal instantiation to ∀x(P(x))?
P(x) for some specific x
P(x) for all x
∃x(P(x))
P(x)∨¬P(x)
If f:A→B is a bijection, then...
f is injective but not surjective
f is surjective but not injective
f is both injective and surjective
f is neither injective nor surjective
Which of the following is an example of a one-to-one function?
f(x)=x^2 over all real numbers
f(x)=x+2 over real numbers
f(x)=sin(x) over [0,2π]
f(x)=|x| over all real numbers
Which property does a binary operation * satisfy if a*b=b*a for all a,b?
Associativity
Commutativity
Distributivity
Reflexivity
What is the Cartesian product A×B if A={1,2} and B={x,y}?
{1,x,y,2}
{(1,x),(1,y),(2,x),(2,y)}
{(1,1),(2,2)}
None of the above
If f(x)=x^2 and g(x)=2x, what is (f∘g)(x)?
2x^2
(2x)^2
x^4
x^2
Convert 0.1012 into decimal.
0.5
0.625
0.75
0.1
What is the binary representation of 0.25?
0.1
0.01
0.001
0.111
What is the Gray code equivalent of 110?
1010
1001
1110
1011
Perform the subtraction 1012−0102 using 2’s complement.
0110
0010
1110
0100
Which of the following is not a valid octal number?
75
100
9
7
Simplify (A+B)⋅(A+¬B).
A
A⋅B
A+B
A⋅¬B
If a NAND gate has inputs A=1, B=1, what is the output?
0
1
Undefined
Depends on previous states
Which circuit can implement an XOR gate?
A⋅¬B+¬A⋅B
A+B
A⋅B
¬A⋅¬B
What is the dual of A+B=1?
A⋅B=1
A⋅B=0
A+B=0
¬A+B=1
How many rows does a truth table have for 3 variables?
4
6
8
16
What is the probability of rolling a number greater than 4 on a 6-sided die?
1/2
1/3
1/6
2/3
A bag contains 3 red and 2 blue balls. What is the probability of picking a red ball?
1/2
3/5
2/5
1/3
In a four-variable K-map, what does it mean when a group of "1s" is combined with adjacent "Don't Care" cells?
The "Don't Care" cells are ignored.
The "Don't Care" cells become "0s."
The group size increases, simplifying the logic further.
The group size decreases for accuracy.
How does the placement of variables in a K-map influence simplification?
It has no effect on simplification.
It helps identify redundant terms.
It only affects the aesthetic layout.
It ensures no overlaps in groups.
How many permutations of the word DISCRETE can be formed if all letters are distinct?
8!
8!/2!
7!
8!/3!
A box contains 5 red, 4 blue, and 3 green balls. How many ways can 4 balls be chosen if at least one must be red?
C (12,4)
C (12,4) − C (7,4)
C (12,4) − C (9,4)
C (9,4)
In how many ways can a group of 5 students and 3 teachers be arranged in a row if the teachers must sit together?
6! ⋅ 3!
5! ⋅ 3!
7! ⋅ 3!
8! ⋅ 3!
If a fair die is rolled three times, what is the probability of rolling the number "6" exactly once?
1/216
15/216
75/216
125/216
Two cards are drawn from a deck of 52 cards without replacement. What is the probability that both cards are kings?
1/1326
1/221
1/169
1/26
For a relation to be an equivalence relation, it must satisfy:
Reflexivity, symmetry, and transitivity
Reflexivity, symmetry, and antisymmetry
Transitivity, symmetry, and asymmetry
Reflexivity, asymmetry, and transitivity
Which of the following is an example of an irreflexive relation?
"Is a friend of"
"Is a parent of"
"Is equal to"
"Is taller than"
A committee of 4 is to be selected from 6 men and 5 women. How many committees can be formed if there must be exactly 2 men and 2 women?
C (6,2) + C (5,2)
C (6,2) ⋅ C (5,2)
C (11,4)
C (6,4) + C (5,4)
If a set A has 5 elements, the Cartesian product A × A has (a) elements.
A relation that is reflexive, symmetric, and transitive is called a(n) (a) .
The purpose of a "Don't Care" condition in K-map simplification is to allow the inclusion or exclusion of cells to simplify the (a) .
A K-map group that eliminates all variables consists of (a) cells.
The number of variables involved in a Karnaugh map directly influences the size of the (a) used to represent the function.
The Pigeonhole Principle states that if n items are placed into m containers, and n > m, then at least one container must hold more than one (a) .
In permutations, the order of selecting objects is (a) .
The number of ways to arrange n distinct objects is known as a (a) .
Conditional probability is the probability of an event occurring given that another (a) has already occurred.
In a binary relation, the pair (a,b) is said to be related if it satisfies a certain (a) defined by the relation.
