MCASemester 12023-24Discrete MathematicsKCA-104
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Discrete Mathematics (KCA-104) - AKTU Question Paper 2023-24

MCA · Semester 1 · Free PDF Download

This is the official AKTU Discrete Mathematics Previous Year Question Paper for MCA Semester 1, academic session 2023-24. Published by Dr. A.P.J. Abdul Kalam Technical University (AKTU/UPTU), Lucknow. Free PDF download — no login required.

Course:MCA
Semester:Semester 1
Session:2023-24
University:AKTU / UPTU

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Questions Asked in 2023-24

Discrete Mathematics (KCA-104) — complete question paper · 100 marks · 3 Hours

Section AAttempt all q u e s t i o n s i n b r i e f .
  • a
    Define the Cartesian Product of sets with example. 2
  • b
    If set 𝐴has 𝑛 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠 , how many relations are there from𝐴 𝑡𝑜 𝐴 ? 2
  • c
    Draw the Hasse diagram of ሺ𝐷଼ , /ሻ. 2
  • d
    Express the following Boolean function in Sum of minterms
  • e
    Prove the following Equivale nces by using Truth table
  • f
    Define Bound and Free variables with example. 2
  • g
    Define Order of an element of a Group with example 2
  • h
    What do you mean by Even and Odd Permutation? 2 i. State the Mathematical Induction Law. 2 j. Find the minimum number of students in a class so that three o f them are born in the same month
Section BAttempt any three o f t h e f o l l o w i n g :
  • a
    Define the composition of function. If 𝑓ሺ𝑥 ሻ ൌ𝑥 ଶ െ1 𝑎 𝑛 𝑑 𝑔ሺ𝑥ሻ ൌ
  • b
    IF𝐴 ൌ ሺ𝑎, 𝑏, 𝑐ሻ, show thatሺ𝑃 ሺ𝐴ሻ,⊆ ሻ is a Poset and draw its Hasse diagram. 10
  • c
    Rewrite the following argumen t using quantifiers, variables and predicate symbols. Prove the validity of the argument: “If it rains then it will be cold. If it is cold then I shall stay at home. Since it rainstherefore, I shall stay home”
  • d
    Define the Subgroup. Prove that the additive group of even i ntegers is a subgroup of the additive group of all integers
  • e
    Prove that:8௡– 3 ௡ is a multipleof 5for all n≥1by mathematical induction. 10
Section CAttempt any one p a r t o f t h e f o l l o w i n g :
  • a
    In a group of 850 person, 600 can speaks Hindi and 340 can s peak Tamil. Find :i) How many can speak both Hindi and Tamil? ii) How many can speak Hindi only? iii) How many can speak Tamil only?
  • b
    If 𝑅 be the relation on set 𝐴 ൌ ሼ𝑎, 𝑏, 𝑐, 𝑑ሽ a n d𝑅ൌ Determine: i) Reflexive closure of 𝑅, ii) Symmetric closure of 𝑅, iii) Transitive closure of 𝑅
  • a
    Express the Boolean expression: 𝑓ሺ𝑥 , 𝑦 , 𝑧 ሻ ൌ ሺ𝑥ᇱ𝑦ሻᇱሺ𝑥 ൅ 𝑧ሻ in both
  • b
    Use Karnaugh map representation to find minimal sum of produ cts expression for the following Boolean function
  • a
    Prove the following Equivalence:𝑝 → ሺ𝑞 ∨ 𝑟ሻ ≡ ሺ𝑝 → 𝑞ሻ ∨ ሺ𝑝 → 𝑟ሻ 10
  • b
    Obtain the 𝑑𝑖𝑠𝑗𝑢𝑛𝑐𝑡𝑖𝑣𝑒 𝑛𝑜𝑟𝑚𝑎𝑙 𝑓𝑜𝑟𝑚ሺ𝐷𝑁𝐹ሻ of the following logical expression:𝑝→ ሺሺ𝑝 → 𝑞ሻ ∧ ∼ ሺ∼ 𝑞 ∨ ∼ 𝑝ሻ
  • a
    If the Inverse of an element “𝑎” in a group is "𝑎ିଵ" , then the Inverse
  • b
    Show that the set of fourth r oots of unity forms an abelian group with respect to multiplication
  • a
    Solve the following Recurrence Relation
  • b
    What do mean by Generating f unction. Find the Generating fun ction of the following series:1,1,1,1,1,1,1

Question text is extracted from the official AKTU question paper PDF above. Hindi translations are omitted — every question is printed in English in the original paper. Last verified: 2026-08-23.

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