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WorksheetsMFCA Quiz Units 1 to 4
Total questions: 20
Worksheet time: 36mins
What principle is associated with the operations of sets?
Pigeonhole Principle
Principle of Inclusion
Principle of Exclusion
Principle of Distribution
Which of the following is a type of probability distribution?
Discrete Probability Distribution
Linear Probability Distribution
Quadratic Probability Distribution
Cubic Probability Distribution
Which type of relation is characterized by having a specific property of symmetry?
Equivalence Relation
Transitive Relation
Reflexive Relation
Irreflexive Relation
In a group of 100 students, 60 like Mathematics, 45 like Physics, and 30 like both Mathematics and Physics. How many students like either Mathematics or Physics?
75
85
90
100
In a room of 367 people, how many people are guaranteed to have the same birthday (assuming 365 days in a year, ignoring leap years)?
1
2
3
atleast 2
A random variable X takes values {0,1,2,3} with probabilities P(X=0)=0.1, P(X=1)=0. 2, P(X=2)=0. 3, and P(X=3)=0.4. What is E(X) (the expected value of X)?
1.5
1.7
2.0
2.2
Given a discrete random variable X with mean E(X)= 5 and E(X2)= 31, what is the variance of X?
5
6
7
8
Which of the following experiments follows a binomial distribution?
Rolling a fair die once
Flipping a coin 5 times and counting heads
Measuring the weight of a fruit
Choosing a random number between 1 and 100
A normal distribution is:
Always skewed to the right
A distribution with only discrete values
Always skewed to the left
A symmetric bell-shaped curve
Which of the following is a proposition?
5+3 =8
What is your name?
Please Close the Door
Lets go to park
What is the result of p∨¬p (p OR NOT p)?
Undefined
Always false
Always true
Sometimes true, sometimes false
Rules of Inference
If "All humans are mortal" and "Socrates is a human", what can be concluded using modus ponens?
Socrates is mortal
Socrates is immortal
Socrates is not a human
Nothing can be concluded
Which of the following is the contrapositive of the statement:
If the ground is wet, then it rains.
If it does not rain, then the ground is not wet.
If the ground is not wet, then it does not rain.
If the ground is wet, then it does not rain.
Which of the following statements is equivalent to:
∀x∃y (x+y=10)
For every x, there exists a y such that their sum is 10.
There exists a number y such that for all x, their sum is 10
There exists an x such that for all y, their sum is 10.
The sum of all numbers is always 10.
Rules of Inference:
Suppose we know that:
1) P⇒Q is true.
2) Q⇒R is true. and
3) P is true.
What can we conclude?
R is true.
Q is false.
P is false.
.
R is false
A relation R on a set A is called antisymmetric if:
(a,b)∈R and (b,a)∈R implies a=b
(a,b)∈R and (b,a)∈R for all a,b∈ A
(a,b)∈R implies (b,a)∈R
(a,a)∈R for all a∈ A
Let R be a reflexive relation on a set A with n elements. What must be true about its relation matrix?
All diagonal entries are 0
The matrix is symmetric
All diagonal entries are 1
The matrix has only 1s
A partial order is a relation that is:
Reflexive, symmetric, and transitive
Reflexive, antisymmetric, and transitive
Antisymmetric and symmetric
Symmetric and transitive
Let R be an equivalence relation on a set A. Which of the following is always true?
The equivalence classes of R form a partition of A
R is always antisymmetric
R is always irreflexive
R is a partial order
Which of the following is a valid example of a partial order?
The "is parallel to" relation between two lines in geometry
The "is a friend of" relation on a group of people
The "divides" relation (a∣b) on the set of positive integers
The "has the same birthday as" relation on a set of students
