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{F} Show that the following logical equivalences hold for the
Peirce arrow ↓, where P ↓ Q ≡ ∼(P ∨ Q).
a. ∼P ≡ P ↓ P
b. P ∨ Q ≡ (P ↓ Q) ↓ (P ↓ Q)
c. P ∧ Q ≡ (P ↓ P) ↓ (Q ↓ Q)
H d. Write P → Q using Peirce arrows only.
e. Write P ↔ Q using Peirce arrows only.
{F} Show using the rules of resolution/inference, that no
single assignment of truth values to p, q, r makes all
the disjunctions p V-9, p V-9,9 V r,
qVT, V revaluate to true. Proof using truth
na
{F} How many different sequences, each of length r, can be formed using elements
from A if
(a) elements in the sequence may be repeated?
(b) all elements in the sequence must be distinct?
an + an-1 - 10an-2 + 8an-3
An online shopping platform has given two types of saving to its members who have completed 2 doses of vaccination for Covid-19 when they purchase the products online, which are either discount of 15% or cashback of 15%. For the selection of saving for their purchase, a member can only choose either discount or cashback but not both of them. The saving entitlement is shown in Table 2. By using an appropriate logical operator to combine the choices made for the types of saving, the entitlement of the saving is shown in Table 1. By using the Raptor, produce a flow chart that performs the following procedures:
Each of 39 of my friends has either a dog a cat or a rabbit each of 24 of them has a dog each of 17 gas a cat and each of 16 has a rabbit the number having both a dog and a cat is one more than the number having both a cat and a rabbit while 2of them have all the three how many of my friends have both a rabbit and cat
Draw a simple, undirected graph yourself, the vertices are connected with each other including 8 vertices and 14 edges. Find the shortest path from two arbitrary vertices:
a) The weight of each edge is 1.
b) Self-weighting for edges
State TRUE or FALSE justifying your answer with proper reason.
a. 2𝑛^2 + 1 = 𝑂(𝑛^2 )
b. 𝑛^2 (1 + √𝑛) = 𝑂(𝑛^2 )
c. 𝑛^2 (1 + √𝑛) = 𝑂(𝑛^2 log 𝑛)
d. 3𝑛^2 + √𝑛 = 𝑂(𝑛 + 𝑛√𝑛 + √𝑛)
e. √𝑛 log 𝑛 = 𝑂(𝑛)
Assume that the function y(x) = f (x) + g(x) has a single local minimum in the
interval 0 <= x <= 1, at x = xm. Write
(i) a function M-file (called funct.m) and
(ii) a MATLAB statement (using the fminbnd command)
that together will compute xm and the value of y at xm.
Suppose you want to encode messages containing only the following characters with their given respective frequencies: B: 55 D: 15 E: 80 G: 5 U: 45
(a) What is the minimum length bit string required to encode each character with a distinct, fixed-length code?
(b) Construct the Huffman Tree for the characters with the given frequencies. (Use the convention that when merging two vertices, the vertex with the largest count goes on the left.)
(c) Use your Huffman Tree to decode the message M = 00101010000011
(d) How many bits are required to encode the characters with the given frequencies using the Huffman Encoding and the fixed-length encoding you found in part (a)? How much storage savings does this represent?
