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Discrete Mathematics

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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 3.9 years ago by krithikkm200 • 10
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Draw the Hasse diagram of $L_1 \times L_2$ with product partial order.
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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Let A={1, 2, 3, 4} and R={(1, 2), (2, 3), (3, 4), (2, 1)}. Find the transitive closure using Warshall's algorithm.
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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Let R be a relation on the set of Integers Z defined by aRb if and only if a $\equiv m (m0d 5)$. Prove that R is an equivalence relation. Find Z/R.
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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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 3.9 years ago by krithikkm200 • 10
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Show that a relation is reflexive and circular if and only if it is an equivalence relation.
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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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 3.9 years ago by krithikkm200 • 10
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Show that $A-(B-C)=(A-B) \cup ( A \cap B \cap C)$
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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It was found that in a class, 80 students are passed in English, 60 in Science and 50 in Mathematics. It was also found that 30 students passed in both English and Science, 15 students passed in both
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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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 3.9 years ago by krithikkm200 • 10
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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 3.9 years ago by krithikkm200 • 10
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Prove by mathematical induction $^n-y^n$ is divisible by x-y.
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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Prove that $8^n - 3^n$ is a multiple of 5 by mathematical Induction, n>=1.
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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Use the laws of logic to determine the following expression as tautology or contradiction.
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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Use the laws of logic to show that $[(p \rightarrow q) \hat \ \ \ \sim q]\rightarrow \sim p$ is tautology.
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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Prove p^ (qVr) and (p^ q)V(p^r) are logically equivalent.
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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$6^{n+2}+ 7^{2n+1}$ is divisible by 43.
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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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 3.9 years ago by krithikkm200 • 10
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Use the laws of logic to show that $[(p \rightarrow q) \hat \ \ \ \sim q]\rightarrow \sim p$ is tautology.
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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Show that $[(p \rightarrow q) \hat \ \ \ \sim q]\rightarrow \sim p$ is tautology.
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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By using mathematical induction prove that $1+ a + a^2+....a^n =\dfrac{1-a^{n+1}}{1-a}$ , where n>=0.
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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Let A=(a, b, c). Show that (P{A}, C) is a poset. Draw its Hasse Diagram. P(A) is the power set of A.
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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Draw the Hasse diagram of $D_{60}$. Also find whether it is a lattice.
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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Define Distributive Lattice along with one appropriate example.
discrete mathematics updated 3.9 years ago by krithikkm200 • 10
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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 3.9 years ago by krithikkm200 • 10
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