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WorksheetsDiscrete Structure (COS 203) CA
Total questions: 40
Worksheet time: 44mins
Convert hexadecimal 5C3 to a decimal value.
1475
1575
1675
1775
Determine the two's complement for hexadecimal value 4B.
4A
B5
4B
A5
Which of the following options is the appropriate representation for such A is a subset of B and A might be equal to B.
A ⊆ B
A ∉ B
A ⊂ B
A ∅ B
Let A = {9, 10, 11, 12, 13, 14, 15} and B = {14, 15, 16, 17, 18, 19}. Find the result for A ∪ B.
{9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}
{9, 10, 11, 17, 18, 19}
{14, 15}
{10, 11, 12, 13, 14, 15, 16, 17, 18}
Given F = {3, 5, 6, 7, 9, 11}, G = {2, 4, 6, 7, 10}, H= {3, 4, 7, 12}, determine the symmetric for F union G.
{3,4, 6, 7}
{2, 3, 6, 10, 12}
{6, 7}
{2, 3, 4, 5, 6, 7, 9, 10, 11}
Given X = { 1, 4, 6, 8, 12}, Y = { 1, 2, 4, 5, 6, 7, 8}, Z = {1, 3, 5, 6, 7, 8, 9, 11}, determine the difference of Y - Z
{1, 3, 5, 6, 7, 8}
{1, 3, 5, 9, 11}
{2, 4}
{9, 11}
"It’s raining and it’s not raining" is an example of
Contradiction
Tautology
Valid sentence
None of the above
Truth tables are used to define
Logical Connectives
Logics
symbols
Tabular form
The science or study of how to evaluate arguments and reasoning
Logic
Discrete
Mathematics
Symbolic
What type of logic is this table showing:
AND
OR
NOR
XOR
Which equation represents the union of sets A and B?
A (intersect symbol) B
A X B
A U B
A - B
Let A be the set {red, blue, green} and B is the set {yellow}, what is A X B? In other words, what is the cartesian product of A X B?
{red, yellow} , {blue, yellow} , {green, yellow}
{red}, {blue}, {green}, {yellow}
{red, blue, green, yellow}
{red, blue}, {green, yellow}
If a password consists of 4 letters followed by 2 digits, how many possible passwords can be made?
26*4*10^2
26*4*10*2
26*10*4
26*4+10^2
What is the value of 5P3 (permutation of 5 items taken 3 at a time)?
20
60
120
10
How many ways can a committee of 4 be selected from 10 people?
10P4
10C4
4C10
10*4
What is the value of 8C2?
16
28
56
112
What is the total number of outcomes when rolling three six-sided dice?
6
18
216
1296
A bag contains 4 red balls, 3 blue balls, and 2 green balls. What is the probability of randomly selecting a blue ball?
1/3
3/9
3/4
1/4
A relation is symmetric if:
(𝑎,𝑏)∈𝑅⟹(𝑏,𝑎)∉𝑅(a,b)∈R⟹(b,a)∈/R
(a,b)∈R⟹(b,a)∈R
(a,a)∈R∀a∈A
None of these
If a four-variable K-map group covers four adjacent cells, what simplification occurs?
Two variables are eliminated
One variable is eliminated
No variables are eliminated
All variables are eliminated
If a four-variable K-map group covers four adjacent cells, what simplification occurs?
Two variables are eliminated
One variable is eliminated
No variables are eliminated
All variables are eliminated
What is the main advantage of using a K-map for simplification?
Eliminates the need for Boolean algebra
Ensures maximum literals in the expression
Visually identifies redundancies
Avoids the need for truth tables
How many groups can be formed from "Don't Care" conditions in a three-variable K-map?
1
2
Multiple groups
No groups
Which type of K-map group eliminates two variables in a simplified expression?
Pair
Quad
Octet
Single
What is the largest group of cells that can be formed in a four-variable K-map?
4
8
12
16
How many adjacent cells does a single cell in a four-variable K-map have?
2
3
4
5
Which property is violated if aRb and bRa, but a≠b?
Reflexivity
Symmetry
Transitivity
Anti-symmetry
Which of the following represents the intersection of sets L and M?
Given that L = {1, 2, 3, 4, 5} and M = {4, 5, 6, 7}
{1, 2, 3, 4, 5, 6, 7}
{4, 5}
{1, 2, 3, 4}
{1, 2, 3, 4, 5}
What is the primary focus of discrete mathematics?
Complex numbers
Real analysis
Discrete structures and objects
Continuous functions
Which proof technique involves assuming the opposite of what you want to prove?
Direct proof
Proof by induction
Proof by contradiction
Constructive proof
What does the pigeonhole principle state?
If you have more pigeons than holes, at least one hole must contain more than one pigeon.
All pigeons must be placed in separate holes.
Pigeons can only be placed in one hole.
If you have more holes than pigeons, each hole can hold one pigeon.
In propositional logic, what does the symbol '¬' represent?
And
Or
Not
If and only if
What is the cardinality of the set {1, 2, 3, 4}?
3
2
4
5
What is the result of the operation A ∪ B?
Elements common to both A and B
Elements in A or B or both
Elements in A but not in B
Elements in B but not in A
Which of the following statements is true about a predicate?
It contains a variable.
It is always true.
It is a simple statement.
It cannot be expressed as a function.
What does the binomial theorem relate to?
Counting permutations
Counting combinations
Expanding powers of binomials
Finding limits
