Dr.A.P.J.Abdul Kalam University BE - IT III SEM Discrete Structures [IT-224] Dec - 2020 Question Paper

 Dr.A.P.J.Abdul Kalam University

Bachelor of Engineering

Third Semester Main Examination, Dec-2020

Discrete Structures [IT-224]

Branch-IT

Time: 3:00 Hrs Max Marks 70

Note : Attempt any five questions. All questions carry equal marks.

Q.1 (a) Describe Graph and its types?

 (b) State and prove binomial theorem?

Q.2 (a) Define - Graph, Degree of a vertex, Even and odd vertex, Degree of Graph, Path.

 (b) Define – (A) Ring, (B) Field

Q.3 (a) State and prove binomial theorem.

 (b) State and prove recurrence relations.

Q.4 (a) Describe Finite State Machine.

 (b)Define Lattice and describe types of lattice.

Q.5 (a) Represent on truth table: ~ (𝑝 ∧ ~𝑞 )

(b) Let 𝐺 = {1, −1,, −𝑖 }, which forms a group under multiplication and 𝐼 be the group of all

integers under addition, prove that the mapping 𝑓 :𝐼 → 𝐺 such that 𝑓 (𝑥 ) = 𝑖 𝑛 ∀𝑛 ∈𝐼 is a

homomorphism.

Q.6 (a) Show that {1, −1, 𝑖, −𝑖} be the group with respect to multiplication.

(b) A relation R is defined on the set 𝑍 by “𝑎 𝑅 𝑏 𝑖 𝑓 𝑎 – 𝑏 is divisible by 5” for 𝑎 , 𝑏 ∈𝑍 .

Examine if R is an equivalence relation on 𝑍 .

Q.7 (a) Expand (2𝑥 – 5𝑦) 7 with the help of binomial expansion.

 (b) Define - (A) Set, (B) Countable Set, (C) Uncountable Set

Q.8 Short note on: (All define with example)

 (i) Group

(ii) Semi group

(iii) Monoid

(iv) Abelian group.

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