MCASemester 12021-22Discrete Mathematics KCA104
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Discrete Mathematics K (CA104) - AKTU Question Paper 2021-22

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This is the official AKTU Discrete Mathematics K Previous Year Question Paper for MCA Semester 1, academic session 2021-22. 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:2021-22
University:AKTU / UPTU

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Questions Asked in 2021-22

Discrete Mathematics K (CA104) — complete question paper

Section AAttempt all q u e s t i o n s i n b r i e f .
  • a
    What is the cardinality of the set? Find the cardinality of the set {1, {2, ϕ, { ϕ }}, { ϕ }}
  • b
    Let the two following functions be defined on set of real numb ers be as: f(x) = 2x+3 and g(x) = x2+1. Find the (fog)(x)
  • c
    Define the well-ordered set? G ive an example of well-ordered set. 2 2
  • d
    Draw the Hasse diagram of the lattice of (D 6, |). 2 2
  • e
    Define Tautology and Contradiction. 2 3
  • f
    Discuss the truth table of pq . 2 3
  • g
    What is the generator of a cyclic group? 2 4
  • h
    Find the order of each element in the group ({1, -1}, .). 2 4 i. Find the number of handshakes in party of 12 people, where eac h two of them shake hands with each other. j. Discuss the pigeonhole principle? 2 5
Section BAttempt any three o f t h e f o l l o w i n g :
  • a
    Prove that the relation (x, y) ∈ R, if x ≥ y defined on the set of positive integers is a partial order relation
  • b
    If B = {1, 3, 5, 15}, then show that  ,, ,B  .' is a Boolean Algebra, where a + b = lcm (a, b), a .b = gcd (a, b) and 15a a'
  • c
    (i) Prove that conditional proposition and its contrapositive are equivalent, i.e. ሺ𝑝 → 𝑞ሻ ≡ ~𝑞 → ~𝑝. (ii) Prove the equivalence: pq q p q 
  • d
    Show that set ℤ଺ ൌ ሼ0,1,2,3,4,5ሽ forms a group with respect to addition modulo 6
  • e
    (i) State all PEANO’s axioms. (ii)In how many ways, can 7 boys and 5 girls be seated in a row, so that no two girls may sit together?
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 survey of 60 people, it was found that 25 eat Apple, 26 eat Orange and 26 eatBanana fruit. Also 9 eat both Apple and Banana, 11 eat both Orangeand Apple, and 8 eat both Orangeand Banana. 8eat no fruit at all. Then determine i. the number of people who eat all three fruit. ii. the number of people who eat exactly two fruit. iii. the number of people who eat exactly one fruit
  • b
    State and Prove De Morgan’s laws for set theory. 10 1
  • a
    (i)Write the definition of the maximal, minimal, greatest and leas t element of a Poset. (ii)If S = {10, 11, 12}. Determine the power set of S. Draw the Has se diagram of Poset (P(S), (iii)Find the maximal, minimal, greatest and least element of the Poset in Part (ii)
  • b
    i) Determine the DNF of Boolean expression  ,, .f xyz x y z ' ii) Simplify the following Boolean expression using K-Map method: ''' '' ' ' ' 'A B C A B C A BC A BC AB C ABC  
  • a
    (i) Given the value of p → q is false, determine the value of (ii) Prove the equivalence: p qq p q 
  • b
    State and Prove De Morgan’s laws for propositions using trut h table. 10 3
  • a
    Show that set of all integers ℤ forms a group with respect to binary operation * defined as a * b = a + b + 1, where a,b ∈ ℤ
  • b
    (i)Define Ring and Field. Give an example of a Ring and a Field. (ii)Prove that every cyclic group is abelian
  • a
    State Mathematical Induction. Using the Mathematical Inducti on, show that  222 2 1( 2 1 )123. . . , 1 6 nn nnn   
  • b
    Use generating functions to sol ve the recurrence relation, 12 19 20 0 where 3 and 10no nnaa a a a     

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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