Discrete Mathematics
Mahatma Gandhi Central University, Bihar
B.Tech Computer Science & Engineering
Semester 4 Examination, 2025
Discrete Mathematics (CSET3124)
Assessment Questions
Discrete Mathematics (CSET3124) - 2025
SECTION – A
(Multiple Choice Questions – 5 Marks). Attempt all questions. Each question carries 1 mark.
- 1
The proposition [(p ∨ ¬q) → r] ∧ p is:
- 2
How many ways can 5 identical balls be placed into 3 distinct boxes such that each box gets at least one ball?
- 3
The symmetric difference of sets A and B is defined as:
- 4
In a group of 10 people, at least two of them have the same birthday month. This is an example of:
- 5
A graph with no cycles and n vertices must have exactly:
SECTION – B
Attempt ANY TWO questions. (Short Answer Questions – 5 Marks). Each question carries 2.5 marks. Word limit: 150 words.
- 1
Determine the validity of the argument using rules of inference:
P₁ : (p → q) ∧ (¬r → ¬q)
P₂ : r
∴ ?
State the conclusion and justify each step.
- 2
How many 4-digit even numbers can be formed using digits 1 to 9 (with repetition), such that the number is divisible by 4?
- 3
Let A = {1, 2, 3, 4, 5} and R = {(a, b) ∈ A × A | a ≤ b}. Determine whether R is reflexive, antisymmetric, and transitive. Justify.
- 4
Out of 100 students: 60 like Programming, 70 like Mathematics, and 45 like both. Use the inclusion-exclusion principle to find how many students like exactly one of the two subjects.
SECTION – C
Write in 300 Words (Long Answer Questions – 10 Marks). Attempt the questions having an internal choice. Each question carries 5 marks.
- 1
Answer any ONE of the following
(a)A department has 6 men and 5 women. In how many ways can a team of 5 members be formed such that:
(i) It includes at least 3 women?
(ii) One specific man is always included?
Provide clear combinatorial steps.
OR
(b)Find the number of integer solutions to the equation x₁ + x₂ + x₃ = 20 under the constraints: x₁ ≥ 4, x₂ ≥ 5, x₃ ≥ 2. Use the transformation method.
- 2
Answer any ONE of the following
(a)A function f : Z → Z is defined by f(x) = 4x − 7. Prove whether it is one-to-one and onto. Derive the inverse if it exists.
OR
(b)Let A = {1, 2, 3, 4, 5, 6}, and define relation R as aRb if and only if (a − b) is divisible by 3. Prove that R is an equivalence relation. List all equivalence classes.