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}