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Discrete Mathematics

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What is an Universal and existential quantifiers? Prove the distribution law. $p v (q \ \ \ \hat \ \ \ r) \equiv (p v q)\ \ \ \hat \ \ \ (p v r).$
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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Let A={1,2,3,4,6}=B, a R b if and only if a is multiple of b. Find R. Find each of the Following (i) R(4) (ii) R(6) (iii) R({2,4,6}).
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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Find the generating functions for the following sequence (i) 0, 0, 0, 1, 2, 3, 4, 5, 6, 7,............................. (ii) 6, -6, 6, -6, 6, -6, 6,...................
discrete mathematics updated 2.3 years ago by sagarkolekar ★ 11k
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Let S = (1, 2, 3, 4, 5) and A = S X S. Define the following relation R on A: (a, b) R (c, d) if and only if ad = bc. Show that R is an equivalence relation and compute A/R.
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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Show that the (2, 5) encoding function e: $B^2-> B^5$ defined by e(00) = 00000 e(01) = 01110 e (10) = 10101 e (11) = 11011 is a group code. How many errors will it detect and correct?
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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Let R be a relation on Set A= {1, 2, 3, 4}, given as R = {(1, 1), (1, 4), (2, 2), (2, 3), (3, 2), (3, 3), (4, 1), (4, 4)} Find transitive closure using Warshall's Algorithm.
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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Find how many integers between 1 and 60 are (i) not divisible by 2 nor by 3 and nor by 5. (ii) Divisible by 2 but not by 3 and nor by 5.
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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Define distributive lattice. Show that in a bounded distributive lattice, if a complement exists, its unique.
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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What is the total number of vertices in a full binary tree with 20 leaves?
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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$\text{Find the generating function for the following finite sequences} \\1. \ \ \ \ 1, 1, 1, 1, 1, 1,......$
discrete mathematics updated 21 months ago by sagarkolekar ★ 11k
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Determine whether following graphs are isomorphic
discrete mathematics updated 2.3 years ago by sagarkolekar ★ 11k
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Find the complement of each element in D30
discrete mathematics updated 21 months ago by sagarkolekar ★ 11k
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Solve the following recurrence relation: $a_n-7a_{n-1}+10a_{n-2}= 0$ with initial condition $a_0= 1, a_1= 6$.
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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Prove that the set G ={1, 2, 3, 4, 5, 6} is an abelian group under multiplication modulo 7.
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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Find how many integers between 1 and 60 are not divisible by 2 nor by 3 and nor by 5 respectively.
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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Consider an equilateral triangle whose sides are of length 3 units. If ten points are chosen lying on or inside the triangle, then show that at least two of them are no more than 1 unit apart.
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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Discrete Structures. Find the number of integers between 1 and 1000 which are (i) Divisible by 2,3 or 5 (ii) divisible by 3 only but not by 2 nor by 5
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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Let m be the positive integers greater than 1. Show that the relation $R =\{(a,b)|a \equiv b (mod \ \ m)\}$, i.e. aRb if and only if m divides a-b, is an equivalent relation on the set of integers.
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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Consider the (3, 5) group encoding function
discrete mathematics updated 2.3 years ago by sagarkolekar ★ 11k
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Show that if a relation on set A is transitive and irreflexive then it is asymmetric.
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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Prove that the set A= {0,1,2,3,4,5} is a finite Abelian group under addition modulo 6.
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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If 11 people are chosen from a set of A=(1, 2, 3, . . . 20), then one of them is multiple of other.
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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If(G, *) is an Abelian group, then for all $a, b \in G$ show that $(a * b)^n =a^n * b^n$ (use mathematical induction).
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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Let A = {1, 2, 3, 4, 5} and R be the relation defined by a R b if and only if a < b. Compute $R, R^2$ and $R^3$ .Draw digraph of $R, R^2$ and $R^3$.
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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Consider the lattices L1={1, 2, 4}, L2={1, 3, 9} under divisibility. Draw the lattice L1 x L2.
discrete mathematics updated 2.3 years ago by pedsangini276 • 4.8k
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