This blog is designed specially for BSc IT First Year students (Ahmedabad / Gujarat University pattern) and is supported by TOPS Technologies. In this article, we will solve each exam question step‑by‑step, using easy language, clear logic, and real examples, so even beginners can understand the concepts deeply.
📘 Section A – Objective Questions (Solved)
Q1. If A = {1, 2, 3}, how many subsets does A have?
Explanation:
If a set has n elements, the number of subsets is:
[ 2^n ]
Here, n = 3
[ 2^3 = 8 ]
✅ Answer: 8 subsets
Q2. Every relation is a function – True or False?
Explanation:
A relation becomes a function only when each input has exactly one output.
Some relations may have one input linked to multiple outputs.
✅ Answer: False
Q3. Find: (2^3 \times 2^2)
Using exponent rule:
[ a^m \times a^n = a^{m+n} ]
[ 2^3 \times 2^2 = 2^{5} = 32 ]
✅ Answer: 32
Q4. Degree of polynomial: (3x^4 + 5x^2 + 7)
The highest power of x is 4.
✅ Answer: 4
Q5. What is a Null Set?
A set with no elements is called a null set.
Example: { }
✅ Answer: A set containing no elements
Q6. Symbol for Logical AND
Logical AND is represented by:
✅ Answer: ∧
Q7. Vertices in a complete graph K₄
In graph notation, K₄ means 4 vertices.
✅ Answer: 4
**Q8. Contrapositive of:
“If it rains, the ground is wet.”**
Rule:
If P → Q
Contrapositive = ¬Q → ¬P
Answer: If the ground is not wet, then it did not rain.
Q9. What is a Universal Set?
A universal set contains all elements under discussion.
Example: If studying numbers 1 to 10, then U = {1…10}
Q10. Define Binary Relation
A binary relation relates elements of one set to another set.
Example:
A = {1,2}, B = {a,b}
Relation = {(1,a), (2,b)}
📘 Section B – Short Answer Questions (Solved)
Q11. Union and Intersection of Sets
Let A = {1,2,3}
Let B = {3,4,5}
Union (A ∪ B): {1,2,3,4,5}
Intersection (A ∩ B): {3}
Union means all elements, intersection means common elements.
Q12. Function and Its Types
A function assigns one output to each input.
Types:
One‑to‑One
Many‑to‑One
Onto
Into
Q13. Solve: ( \log_2 32 + \log_2 4 )
[ \log_2 32 = 5 ]
[ \log_2 4 = 2 ]
Total = 5 + 2 = 7
Q14. De Morgan’s Laws
( \overline{A + B} = \overline{A} \cdot \overline{B} )
( \overline{A \cdot B} = \overline{A} + \overline{B} )
These laws are very important in logic circuits and programming.
Q15. Matrix and Its Types
A matrix is a rectangular arrangement of numbers.
Types:
Row Matrix
Column Matrix
Square Matrix
Identity Matrix
Q16. Permutation and Combination
Permutation: Order matters
[ nPr = \frac{n!}{(n-r)!} ]
Combination: Order does not matter
[ nCr = \frac{n!}{r!(n-r)!} ]
Q17. Graph Theory and Applications
Graph consists of vertices and edges.
Applications:
Computer Networks
Google Maps
Social Media
Q18. Inverse of Matrix
Matrix:
[
\begin{bmatrix}
1 & 2 \
3 & 4
\end{bmatrix}
]
Determinant = (1×4 − 2×3) = −2
Inverse exists because determinant ≠ 0.
Q19. Proposition and Logical Connectives
A proposition is a statement that is true or false.
Logical connectives:
Q20. Tree in Discrete Mathematics
A tree is a graph with no cycles.
Used in:
File systems
Data structures
📘 Section C – Long Answer Questions (Concept Explained)
Q21. Relations and Types
Relations connect elements of sets.
Types:
Reflexive
Symmetric
Transitive
Q22. Mathematical Induction
Used to prove formulas for all natural numbers.
Steps:
Base Case
Induction Hypothesis
Induction Step
Q23. Boolean Algebra
Used in digital electronics and programming.
Expression:
(A + B)(A + B̄) = A
Q24. Graphs and Applications
Graphs help solve real‑world problems like:
Network routing
Shortest path
Web page ranking
