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Function f(x) = (4x + 3)/(5x - 2). Find $f^{-1}$.
discrete mathematics updated 2.5 years ago by pedsangini276 • 4.8k
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Let A={ 1,2,3,4}and let R={(1,2) (2,3)(3,4)(2,1)}. Find transitive closure of R by using Warshall's algorithm.
discrete mathematics updated 2.5 years ago by pedsangini276 • 4.8k
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State and explain Pigeonhole principle, extended Pigeonhole principle.How many numbers must be selected from the set{1, 2, 3, 4, 5, 6 }to guarantee that at least one pair of these numbers add up to 7?
discrete mathematics updated 2.5 years ago by pedsangini276 • 4.8k
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Explain Pigeonhole principle and Extended Pigeonhole Principle. Show that if 7 colors are used to paint 50 bicycles, at least 8 bicycles will be of same color.
discrete mathematics updated 2.5 years ago by pedsangini276 • 4.8k
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Functions f, g, h are defined on a set, X= {1,2,3} as f= {(1,2) (2,3) (3,1)} g = {(1,2} (2,1) {3,3)) h = {(1, 1 ) (2,2) (3,1)} (i) Find fog, g o f are they equal ? (ii) Find fogoh and fohog.
discrete mathematics updated 2.5 years ago by pedsangini276 • 4.8k
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Find all solutions of the recurrence relation $a_n=5a_{n-1}+6a_{n-2}+7^n$
discrete mathematics updated 2.5 years ago by pedsangini276 • 4.8k
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Show that if a relation on set A is transitive and irreflexive then it is asymmetric.
discrete mathematics updated 2.5 years ago by pedsangini276 • 4.8k
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R is the set of real number.
discrete mathematics updated 2.5 years ago by pedsangini276 • 4.8k
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Solve the recurrence relation $a_n=-3(a_{n-1}+a_{n-2})-a_{n-3}$ with $a_0=5, a_1=-9$ and ` $a_2=15$.
discrete mathematics updated 2.5 years ago by pedsangini276 • 4.8k
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Solve the recurrence relation $a_r=3a_{r-1}+2, r > =1$ with $a_0= 1$, using generating function.
discrete mathematics updated 2.5 years ago by pedsangini276 • 4.8k
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$\text{Solve the following recurrence relation:} \\ a_n-5a_{n-1}+6a_{n-2}=0 \\ a_n-5a_{n-1}+6a_{n-2}=2^\pi \text{with initial conditions}a_0 = -1 \ \ and \ \ a_1 =1$
discrete mathematics updated 2.5 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 2.5 years ago by pedsangini276 • 4.8k
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Let H= $\begin{bmatrix} 1&0&0 \\ 0&1&1 \\ 1&1&1 \\ 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{bmatrix}$ be parity check matrix.
discrete mathematics updated 2.5 years ago by pedsangini276 • 4.8k
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Decode the following words relative to a maximum likelyhood decoding function. i)11001 ii) 01010 iii) 00111
discrete mathematics updated 2.5 years ago by pedsangini276 • 4.8k
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Prove that {G, *} is a group.
discrete mathematics updated 2.5 years ago by pedsangini276 • 4.8k
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Define injective, surjective and bijective functions. If R-> R and g:R->R defined by $f(x)= x + 2 \ \ and \ \ g(x) = x^2$. Find i) f o g o f ii) g o f o g
discrete mathematics updated 2.5 years ago by yashbeer ★ 11k
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Consider the region shown below. It is bounded by a regular hexagon whose sides are the length 1 units.
discrete mathematics updated 2.5 years ago by sagarkolekar ★ 11k
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Draw the Hasse Diagram of the following: 1. $D_{105}$ 2. $D_{72}$
discrete mathematics updated 2.5 years ago by sagarkolekar ★ 11k
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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 2.5 years ago by pedsangini276 • 4.8k
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If f:$A \rightarrow B$ be both one-to-one and onto, the prove that $f^{-1}: B \rightarrow A$ is also both one-to-one and onto.
discrete mathematics updated 2.5 years ago by pedsangini276 • 4.8k
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Show that $A \times (B \cap C) = (A \times B) \cap (A \times C)$
discrete mathematics updated 2.5 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 2.5 years ago by pedsangini276 • 4.8k
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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 2.5 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 2.5 years ago by pedsangini276 • 4.8k
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Let s={1, 2, 3, 4} and A=S X S. define the following relation:- R on A : (a, b)R (a', b') if only if a+b=a'+b'. (i) Show that r is an equivalence relation. (ii) Compute A/R
discrete mathematics updated 2.5 years ago by pedsangini276 • 4.8k
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