Course Content
How to watch video course and download study material from enrolled courses?
0/2
How to watch video courses?
01:40
How to download Study Materials (PDF) from the enrolled courses?
01:21
Module-1 of Model Paper-1 (Explained with solutions)
0/7
Introduction
01:11
1a] Show that the compound proposition ——— for primitive statements p, q, r is logically equivalence.
05:38
1b] Establish the validity of the following argument using the Rules of Inference: {p ∧ (p → q) ∧ (s ∨ r) ∧ (r →∼ q)} ⟶ (s ∨ t)
05:20
1c] For the universe of all integers, let p(x), q(x), r(x), s(x) and t(x) denote the following open statements: p(x): x>0, q(x): x is even, r(x): x is a perfect square, s(x): x is divisible by 3, t(x): x is divisible by 7. Write the following statements in symbolic form: i) At least one integer is even. ii) There exists a positive integer that is even. iii) If x is even, then x is not divisible by 3. iv) No even integer is divisible by 7. v) There exists even integer divisible by 3.
04:24
2a] Define a tautology. Prove that, for any propositions p, q, r the compound propositions, {(p→q)∧(q→r)}→{(p→r)} is tautology.
05:40
2b] Prove the following using laws of logic: p→(q→r)⇔(p∧q)→r.
02:58
2c] Give i) direct proof ii) indirect proof iii) proof by contradiction for the following statement: “if n is an odd integer then n+9 is an even integer”.
06:20
Module-2 of Model Paper-1 (Explained with solutions)
0/2
3a] Prove that 1 2 + 32 + 52 + ⋯ . +(2n − 1) 2 = n(2n+1)(2n−1) 3 by Mathematical Induction. 3b]Let a0 = 1, a1 = 2, a2 = 3 and an = an−1 + an−2 + an−3 for n≥3. Prove that an ≤ 3n ∀ n ∈ z+. 3c] Find the number of ways of arrangement of the letters of the word ‘TALLAHASSEE’ which have no adjacent A’s.
14:24
4a] Determine the coefficient of xyz 2 in the expansion of (2x − y − z) 4 . 4b] In how many ways one can distribute 8 identical marbles in 4 distinct containers so that i) no container is empty ii) the fourth container has an odd number of marbles in it. 4c] How many positive integers n can we form using the digits 3,4,4,5,5,6,7 if we want n to exceed 5,000,000?
12:51
Module-3 of Model Paper-1 (Explained with solutions)
0/2
5a] Let f: R → R be defined by, f(x) = { 3x − 5 if x > 0 1 − 3x if x ≤ 0 . Find f −1(0), f−1(1), f−1(−1), f−1(3), f−1(6), f −1([−6, 5]) and f −1([−5, 5]) 5b] State Pigeon hole principle. Prove that in any set of 29 persons; at least 5 persons have been born on the same day of the week. 5c] Let A={1,2,3,4,6} and ‘R’ be a relation on ‘A’ defined by aRb if and only if “a is multiple of b” represent the relation ‘R’ as a matrix, draw the diagraph and relation R.
15:32
6a] If f:A→B, g:B→C, h:C→D are three functions, then Prove that h∘(g∘f)=(h∘g)∘f. 6b] Show that if n+1 numbers are chosen from 1 to 2n then at least one pair add to 2n+1. 6c] Draw the Hasse diagram representing the positive divisors of 72.
20:54
Module-4 of Model Paper-1 (Explained with solutions)
0/2
7a] In how many ways the 26 letters of English alphabet are permuted so that none of the pattern’s CAR, DOG, PUN or BYTE occurs 7b] Define Derangement. In how many ways can each of 10 people select a left glove and a right glove out of a total of 10 pairs of gloves so that no person selects a matching pair of gloves? 7c] Solve the recurrence relation: Cn = 3Cn−1 − 2Cn−2, for n ≥ 2, given C1 = 5, C2 = 3.
14:32
8a] In how many ways one can arrange the letters of the word CORRESPONDENTS so that there are i) exactly 2 pairs of consecutive identical letters? ii) at least 3 pairs of consecutive identical letters? iii) no pair of consecutive identical letters? 8b] Find the rook polynomial for the chess board as shown in the figure 8c] Solve the recurrence relation an+2 − 3an+1 + 2an = 0, a0 = 1, a1 = 6.
22:43
Module-5 of Model Paper-1 (Explained with solutions)
0/2
9a] If H, K are subgroups of a group G, prove that H ∩ K is also a subgroup of G. Is H ∪ K a subgroup of G. 9b] Define Klein 4 group. Verify A = {1, 3, 5, 7} is a klein 4 group. 9c] State and prove Lagrange’s Theorem.
14:54
10a] Show that i) the identity of G is unique. ii) the inverse of each element of G is Unique. 10b] Show that (A, ∙) is an abelian group where A = {a ∈ Q|a ≠ −1} and for any a, b ∈ A, a . b = a + b + ab. 10c] Let G = S4, for α = (1 2 3 2 3 4 4 1 ), find the subgroup H = 〈α〉. Determine the left cosets of H in G.
18:32
DISCRETE MATHEMATICAL STRUCTURES || BCS405A || Model Question Paper-1 with solutions (EXPLAINED)|| 2022 scheme || Video course with study materials
Previous
Next
Join the conversation
Sonar Ritesh 4 months ago
Next video not coming
Reply
0% Complete

Want to earn money while learning? check out our refer and earn program

click here
Any doubts?
Call us immediately

Follow us on social media for regular updates

Instagram Linkedin Youtube

Quick Links

"At LearnyHive, we help students with the essential last-minute preparation they need to clear their semester exams and provide tutors with the platform they deserve."
"At LearnyHive, we help students with the essential last-minute preparation they need to clear their semester exams and provide tutors with the platform they deserve."
Amar Karthik Co-Founder & CTO

Tutorials

Instagram Linkedin Youtube
Copyright © LearnyHive.com 2024. All rights reserved.
Designed, Developed and Maintained by UnikBrushes
Terms, Privacy Policy, Cookies Policy, Refund Policy