Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
8th Edition
ISBN: 9781259676512
Author: Kenneth H Rosen
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 8.6, Problem 27E
Prove Theorem 1.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
2. Claim events on a portfolio of insurance policies follow a Poisson process with parameter
A. Individual claim amounts follow a distribution X with density:
f(x)=0.0122re001, g>0.
The insurance company calculates premiums using a premium loading of 45%.
(a) Derive the moment generating function Mx(t).
4. Find the general solution and the definite solution for the following differential equations:
(a)
+10y=15, y(0) = 0;
(b) 2 + 4y = 6, y(0) =
5) For each function represented by an equation, make a table and plot the corresponding
points to sketch the graph of the function.
(a) y = 75 ()*
220
X
y
200-
-2
180
160
-1
140
0
120
100
1
60
80
2
3
4
x
(b) y = 20 ()*
1
60
40
20
20
0
2
3
65-
-1
X
y
60
-2
55-
50
45
44
40
0
35-
30
1
25
2
20
20
15
3
10
5
LO
4
3-2
T
-1
0
5-
4-
-3-
2-
Chapter 8 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
Ch. 8.1 - Use mathematical induction to verify the formula...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - A vending machine dispensing books of stamps...Ch. 8.1 - A country uses as currency coins with values of 1...Ch. 8.1 - How many was are there to pay a bill of 17 pesos...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - a) Find a recurrence relation for the number of...
Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - Messages are transmitted over a communications...Ch. 8.1 - A bus driver pays all tolls, using only nickels...Ch. 8.1 - a) Find the recurrence relation satisfied by Rn,...Ch. 8.1 - a) Find the recurrence relation satisfied by Rn,...Ch. 8.1 - a) Find the recurrence relation satisfied by Sn,...Ch. 8.1 - Find a recurrence relation for the number of bit...Ch. 8.1 - How many bit sequences of length seven contain an...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - Show that the Fibonacci numbers satisfy the...Ch. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - a) Use the recurrence relation developed in...Ch. 8.1 - In the Tower of Hanoi puzzle, suppose our goal is...Ch. 8.1 - Exercises 33-37 deal with a variation of the...Ch. 8.1 - Exercises 33-37 deal with a variation of the...Ch. 8.1 - Prob. 35ECh. 8.1 - Exercises 33-37 deal with a variation of the...Ch. 8.1 - Prob. 37ECh. 8.1 - Prob. 38ECh. 8.1 - Show that the Reve’s puzzle with four disks can be...Ch. 8.1 - Prob. 40ECh. 8.1 - Show that if R(n) is the number of moves used by...Ch. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Prob. 47ECh. 8.1 - Prob. 48ECh. 8.1 - Show that an2=an2an+2an .Ch. 8.1 - Prob. 50ECh. 8.1 - Prob. 51ECh. 8.1 - Prob. 52ECh. 8.1 - Construct the algorithm described in the text...Ch. 8.1 - Use Algorithm 1 to determine the maximum number of...Ch. 8.1 - For each part of Exercise 54, use your algorithm...Ch. 8.1 - In this exercise we will develop a dynamic...Ch. 8.1 - Dynamic programming can be used to develop an...Ch. 8.2 - Determine which of these are linear homogeneous...Ch. 8.2 - Determine which of these are linear homogeneous...Ch. 8.2 - Solve these recurrence relations together with the...Ch. 8.2 - Solve these recurrence relations together with the...Ch. 8.2 - Prob. 5ECh. 8.2 - Prob. 6ECh. 8.2 - Prob. 7ECh. 8.2 - A model for the number of lobsters caught per year...Ch. 8.2 - Prob. 9ECh. 8.2 - Prob. 10ECh. 8.2 - The Lucas numbers satisfy the recurrence relation...Ch. 8.2 - Find the solution to an=2an1+an2+2an3 for n = 3,4,...Ch. 8.2 - Find the solution to an=7an2+6an3 with a0=9,a1=10...Ch. 8.2 - Find the solution to an=5an24an4 with...Ch. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - Prove this identity relating the Fibonacci numbers...Ch. 8.2 - Solve the recurrence relation an=6an112an2+8an3...Ch. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - Prob. 21ECh. 8.2 - What is the general form of the solutions of a...Ch. 8.2 - Consider the nonhomogeneous linear recurrence...Ch. 8.2 - Consider the nonhomogeneous linear recurrence...Ch. 8.2 - a) Determine values of the constants A and B such...Ch. 8.2 - What is the general form of the particular...Ch. 8.2 - What is the general form of the particular...Ch. 8.2 - a) Find all solutions of the recurrence relation...Ch. 8.2 - Prob. 29ECh. 8.2 - Prob. 30ECh. 8.2 - Find all solutions of the recurrence relation...Ch. 8.2 - Find the solution of the recurrence relation...Ch. 8.2 - Prob. 33ECh. 8.2 - Prob. 34ECh. 8.2 - Find the solution of the recurrence relation...Ch. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Solve the simultaneous recurrence relations...Ch. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - Prob. 45ECh. 8.2 - Suppose that there are two goats on an island...Ch. 8.2 - Prob. 47ECh. 8.2 - Prob. 48ECh. 8.2 - Use Exercise 48 to solve the recurrence relation...Ch. 8.2 - It can be shown that Cn, the average number of...Ch. 8.2 - Prob. 51ECh. 8.2 - Prob. 52ECh. 8.2 - Prob. 53ECh. 8.3 - How many comparisons are needed for a binary...Ch. 8.3 - Prob. 2ECh. 8.3 - Multiply (1110)2 and (1010)2 using the fast...Ch. 8.3 - Express the fast multiplication algorithm in...Ch. 8.3 - Determine a value for the constant C in Example...Ch. 8.3 - Prob. 6ECh. 8.3 - Prob. 7ECh. 8.3 - Suppose that f(n)=2f(n/2)+3 when is an even...Ch. 8.3 - Prob. 9ECh. 8.3 - Find f(n) when n=2k , where f satisfies the...Ch. 8.3 - Give a big-O estimate for the function f in...Ch. 8.3 - Find f(n) when n=3k , where f satisfies the...Ch. 8.3 - Give a big-O estimate for the function f in...Ch. 8.3 - Suppose that there are n=2k terms in an...Ch. 8.3 - How many rounds are in the elimination tournament...Ch. 8.3 - Prob. 16ECh. 8.3 - Suppose that the votes of n people for different...Ch. 8.3 - Suppose that each person in a group of n people...Ch. 8.3 - a) Set up a divide-and-conquer recurrence relation...Ch. 8.3 - a) Set up a divide-and-conquer recurrence relation...Ch. 8.3 - Suppose that the function f satisfies the...Ch. 8.3 - Suppose that the function f satisfies the...Ch. 8.3 - This exercise deals with the problem of finding...Ch. 8.3 - Apply the algorithm described in Example 12 for...Ch. 8.3 - Apply the algorithm described in Example 12 for...Ch. 8.3 - Use pseudocode to describe the recursive algorithm...Ch. 8.3 - Prob. 27ECh. 8.3 - Prob. 28ECh. 8.3 - In Exercises 29-33, assume that f is an increasing...Ch. 8.3 - Prob. 30ECh. 8.3 - Prob. 31ECh. 8.3 - Prob. 32ECh. 8.3 - Prob. 33ECh. 8.3 - In Exercises 29-33, assume that f is an increasing...Ch. 8.3 - In Exercises 29-33, assume that f is an increasing...Ch. 8.3 - In Exercises 29-33, assume that f is an increasing...Ch. 8.3 - In Exercises 29-33, assume that f is an increasing...Ch. 8.4 - Find the generating function for the finite...Ch. 8.4 - Find the generating function for the finite...Ch. 8.4 - In Exercises 3-8, by a closed form we mean an...Ch. 8.4 - In Exercises 3-8, by a closed form we mean an...Ch. 8.4 - Prob. 5ECh. 8.4 - In Exercises 3-8, by a closed form we mean an...Ch. 8.4 - In Exercises 3-8, by a closed form we mean an...Ch. 8.4 - In Exercises 3-8, by a closed form we mean an...Ch. 8.4 - Find the coefficient of x10in the power series of...Ch. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.4 - Use generating functions to determine the number...Ch. 8.4 - Use generating functions to determine the number...Ch. 8.4 - Use generating functions to determine the number...Ch. 8.4 - Use generating functions to find the number of...Ch. 8.4 - In how many ways can 25 identical donuts be...Ch. 8.4 - Use generating functions to find the number of...Ch. 8.4 - Prob. 19ECh. 8.4 - Prob. 20ECh. 8.4 - Prob. 21ECh. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Explain how generating functions can be used to...Ch. 8.4 - Explain how generating functions can be used to...Ch. 8.4 - Prob. 27ECh. 8.4 - Prob. 28ECh. 8.4 - Use generating functions (and a computer algebra...Ch. 8.4 - Use generating functions (and a computer algebra...Ch. 8.4 - Prob. 31ECh. 8.4 - If G(x) is the generating function for the...Ch. 8.4 - Prob. 33ECh. 8.4 - Prob. 34ECh. 8.4 - Prob. 35ECh. 8.4 - Use generating functions to solve the recurrence...Ch. 8.4 - Prob. 37ECh. 8.4 - Use generating functions to solve the recurrence...Ch. 8.4 - Use generating functions to solve the recurrence...Ch. 8.4 - Prob. 40ECh. 8.4 - Prob. 41ECh. 8.4 - Prob. 42ECh. 8.4 - (Calculus required) Let {Cn}be the sequence of...Ch. 8.4 - Use generating functions to prove Pascal’s...Ch. 8.4 - Use generating functions to prove Vandermonde’s...Ch. 8.4 - Prob. 46ECh. 8.4 - Prob. 47ECh. 8.4 - Prob. 48ECh. 8.4 - Find the sequence with each of these functions as...Ch. 8.4 - Find the sequence with each of these functions as...Ch. 8.4 - A coding system encodes messages using strings of...Ch. 8.4 - A coding system encodes messages using strings of...Ch. 8.4 - Generating functions are useful in studying the...Ch. 8.4 - Generating functions are useful in studying the...Ch. 8.4 - Prob. 55ECh. 8.4 - Prob. 56ECh. 8.4 - Generating functions are useful in studying the...Ch. 8.4 - Generating functions are useful in studying the...Ch. 8.4 - Suppose that X is a random variable on a sample...Ch. 8.4 - Prob. 60ECh. 8.4 - Prob. 61ECh. 8.4 - Show that if X and Y are independent random...Ch. 8.5 - How many elements are in A1A2 if there are 12...Ch. 8.5 - There are 345 students at a college who have taken...Ch. 8.5 - A survey of households in the United States...Ch. 8.5 - A marketing report concerning personal computers...Ch. 8.5 - Find the number of elements A1A2A3 if there are...Ch. 8.5 - Prob. 6ECh. 8.5 - There are 2504 computer science students at a...Ch. 8.5 - In a survey of 270 college students, it is found...Ch. 8.5 - How many students are enrolled in a course either...Ch. 8.5 - Find the number of positive integers not exceeding...Ch. 8.5 - Find the number of positive integers not exceeding...Ch. 8.5 - Find the number of positive integers not exceeding...Ch. 8.5 - Find the number of positive integers not exceeding...Ch. 8.5 - Find the number of positive integers not exceeding...Ch. 8.5 - How many swings of length eight do not contain six...Ch. 8.5 - How many permutations of the 26 letters of the...Ch. 8.5 - How many permutations of the 10 digits either...Ch. 8.5 - Prob. 18ECh. 8.5 - Prob. 19ECh. 8.5 - How many terms are there in the formula for the...Ch. 8.5 - Prob. 21ECh. 8.5 - Prob. 22ECh. 8.5 - Prob. 23ECh. 8.5 - Prob. 24ECh. 8.5 - Let E1, E2 ,and E3 be three events from a sample...Ch. 8.5 - Prob. 26ECh. 8.5 - Find the probability that when four numbers from 1...Ch. 8.5 - Prob. 28ECh. 8.5 - Prob. 29ECh. 8.5 - Prob. 30ECh. 8.5 - Prob. 31ECh. 8.6 - Suppose that in a bushel of 100 apples there are...Ch. 8.6 - Prob. 2ECh. 8.6 - Prob. 3ECh. 8.6 - Prob. 4ECh. 8.6 - Find the number of primes less than 200 using the...Ch. 8.6 - Prob. 6ECh. 8.6 - How many positive integers less than 10,000 are...Ch. 8.6 - Prob. 8ECh. 8.6 - How many ways are there to distribute six...Ch. 8.6 - In how many ways can eight distinct balls be...Ch. 8.6 - In how many ways can seven different jobs be...Ch. 8.6 - List all the derangements of {1, 2,3, 4}.Ch. 8.6 - Prob. 13ECh. 8.6 - Prob. 14ECh. 8.6 - A machine that inserts letters into envelopes goes...Ch. 8.6 - A group of n students is assigned seats for each...Ch. 8.6 - Prob. 17ECh. 8.6 - Prob. 18ECh. 8.6 - Prob. 19ECh. 8.6 - Prob. 20ECh. 8.6 - For which positive integers n is Dn, the number of...Ch. 8.6 - Prob. 22ECh. 8.6 - Prob. 23ECh. 8.6 - Prob. 24ECh. 8.6 - Prob. 25ECh. 8.6 - How many derangements of {1, 2, 3, 4, 5, 6} end...Ch. 8.6 - Prove Theorem 1.Ch. 8 - a) What is a recurrence re1aon? b) Find a...Ch. 8 - Explain how the Fibonacci numbers are used to...Ch. 8 - a) Find a recurrence relation for the number of...Ch. 8 - Prob. 6RQCh. 8 - a) Explain how to solve linear homogeneous...Ch. 8 - Prob. 8RQCh. 8 - Prob. 9RQCh. 8 - a) Give a formula for the number of elements in...Ch. 8 - a) Give a formula for the number of elements in...Ch. 8 - Prob. 12RQCh. 8 - Explain how the principle of inclusion-exclusion...Ch. 8 - Prob. 14RQCh. 8 - Prob. 15RQCh. 8 - a) Define a derangement. b) Why is counting the...Ch. 8 - A group of 10 people begin a chain letter, with...Ch. 8 - A nuclear reactor has created 18 grams of a...Ch. 8 - Every hour the U.S. government prints 10,000 more...Ch. 8 - Suppose that every hour there are two new bacteria...Ch. 8 - Messages are sent over a communications channel...Ch. 8 - Prob. 6SECh. 8 - How many ways are there to form these postages...Ch. 8 - Prob. 8SECh. 8 - Solve the recurrence relation an=a2n1/bn2 if a0=1...Ch. 8 - Prob. 10SECh. 8 - Find the solution of the recurrence relation...Ch. 8 - Prob. 12SECh. 8 - Prob. 13SECh. 8 - Prob. 14SECh. 8 - Prob. 15SECh. 8 - In Exercises 15-18 we develop a dynamic...Ch. 8 - In Exercises 15-18 we develop a dynamic...Ch. 8 - In Exercises 15-18 we develop a dynamic...Ch. 8 - Find the solution to the recurrence relation...Ch. 8 - Find the solution to the recurrence relation...Ch. 8 - Give a big-O estimate for the size of f in...Ch. 8 - Find a recurrence relation that describes the...Ch. 8 - Prob. 23SECh. 8 - Prob. 24SECh. 8 - Prob. 25SECh. 8 - Find an where a) an=3 . b) an=4n+7 . c) an=n2+n+1Ch. 8 - Prob. 27SECh. 8 - Prob. 28SECh. 8 - Prob. 29SECh. 8 - Prob. 30SECh. 8 - Prob. 31SECh. 8 - Prob. 32SECh. 8 - Prob. 33SECh. 8 - Prob. 34SECh. 8 - Prob. 35SECh. 8 - How many terms are needed when the...Ch. 8 - How many solutions in positive integers are there...Ch. 8 - How many positive integers less than 1,000,000 are...Ch. 8 - How many positive integers less than 200 are a)...Ch. 8 - How many ways are there to assign six different...Ch. 8 - What is the probability that exactly one person is...Ch. 8 - How many bit stings of length six do not contain...Ch. 8 - What is the probability that a bit string of...Ch. 8 - Prob. 1CPCh. 8 - Prob. 2CPCh. 8 - Prob. 3CPCh. 8 - Prob. 4CPCh. 8 - Prob. 5CPCh. 8 - Prob. 6CPCh. 8 - Prob. 7CPCh. 8 - Prob. 8CPCh. 8 - Prob. 9CPCh. 8 - Prob. 10CPCh. 8 - Prob. 11CPCh. 8 - Prob. 12CPCh. 8 - Given a positive integer n, list all the...Ch. 8 - Prob. 1CAECh. 8 - Prob. 2CAECh. 8 - Find as many prime Fibonacci numbers as you can....Ch. 8 - Prob. 4CAECh. 8 - Prob. 5CAECh. 8 - Prob. 6CAECh. 8 - Prob. 7CAECh. 8 - Prob. 8CAECh. 8 - Prob. 9CAECh. 8 - List all the derangements of 1,2,3,4,5,6,7,8 .Ch. 8 - Prob. 11CAECh. 8 - Find the original source where Fibonacci presented...Ch. 8 - Explain how the Fibonacci numbers arise in a...Ch. 8 - Prob. 3WPCh. 8 - Discuss as mans different problems as possible...Ch. 8 - Prob. 5WPCh. 8 - Prob. 6WPCh. 8 - Prob. 7WPCh. 8 - Prob. 8WPCh. 8 - Describe the solution of Ulam’s problem (see...Ch. 8 - Discuss variations of Ulam’s problem (see Exercise...Ch. 8 - Prob. 11WPCh. 8 - Describe how sieve methods are used in number...Ch. 8 - Look up the rules of the old French card game of...Ch. 8 - Prob. 14WPCh. 8 - Describe the Polyá theory of counting and the kind...Ch. 8 - The problème des ménages (the problem of the...Ch. 8 - Explain how rook polynomials can be used to solve...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- 5. Find the solution to each of the following by using an appropriate formula developed in the lecture slides: (a) + 3y = 2, y(0) = 4; (b) dy - 7y = 7, y(0) = 7; (c) 3d+6y= 5, y(0) = 0arrow_forward1. Evaluate the following improper integrals: (a) fe-rt dt; (b) fert dt; (c) fi da dxarrow_forward8. Given the rate of net investment I(t) = 9t¹/2, find the level of capital formation in (i) 16 years and (ii) between the 4th and the 8th years.arrow_forward
- 9. If the marginal revenue function of a firm in the production of output is MR = 40 - 10q² where q is the level of output, and total revenue is 120 at 3 units of output, find the total revenue function. [Hints: TR = √ MRdq]arrow_forward6. Solve the following first-order linear differential equations; if an initial condition is given, definitize the arbitrary constant: (a) 2 + 12y + 2et = 0, y(0) = /; (b) dy+y=tarrow_forward4. Let A = {a, b, c, d, e, f}, B = {e, f, g, h} and C = {a, e, h,i}. Let U = {a, b, c, d, e, f, g, h, i, j, k}. • Draw a Venn Diagram to describe the relationships between these sets Find (AB) NC • Find (AC) UB Find AUBUC • Find (BC) N (A - C)arrow_forward
- 7. A consumer lives on an island where she produces two goods x and y according to the production possibility frontier x² + y² < 200 and she consumes all the goods. Her utility function is U(x, y) = x y³. She faces an environmental constraint on her total output of both goods. The environmental constraint is given by x + y ≤20. • (a) Write down the consumer's optimization problem. (b) Write out the Kuhn-Tucker first order conditions. (c) Find the consumer's optimal consumption bundle (x*, y*).arrow_forward3. Answer the following questions: (a) Given the marginal propensity to import M'(Y) = 0.1 and the information that M = 20 when Y = 0, find the import function M(Y). (b) Given a continuous income stream at the constant rate of $1,000 per year, what will be the present value II if the income stream terminates after exactly 3 years and the discount rate is 0.04? (c) What is the present value of a perpetual cash flow of $2,460 per year, discounted at r = 8%?arrow_forward5. Let A and B be arbitrary sets. Prove AnB = AUB.arrow_forward
- 2. Answer the following questions: (a) Given the marginal-revenue function R'(Q) = 28Q - €0.3Q, find the total-revenue function R(Q). What initial condition can you introduce to definitize the constant of integration? = (b) Given the marginal propensity to consume C'(Y) 0.80.1Y-1/2 and the information that C = Y when Y = 100, find the consumption function C(Y).arrow_forwardX GG G + C td.bksblive2.com.au/bksblive2/Play... E R New Chrome available CANVAS gmetrix N notion Six big immigratio... >>> All Bookmarks 1.1 ACSF L5 SC Geometry and Measure: Vectors Vectors State the vector quantities shown on the image below. AB = CD' = A B D < C 80 esc F1 F2 F3 F4 ? Help 7arrow_forward7. Let X, A, and B be arbitrary sets such that ACX and BC X. Prove AUB CX.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Propositional Logic, Propositional Variables & Compound Propositions; Author: Neso Academy;https://www.youtube.com/watch?v=Ib5njCwNMdk;License: Standard YouTube License, CC-BY
Propositional Logic - Discrete math; Author: Charles Edeki - Math Computer Science Programming;https://www.youtube.com/watch?v=rL_8y2v1Guw;License: Standard YouTube License, CC-BY
DM-12-Propositional Logic-Basics; Author: GATEBOOK VIDEO LECTURES;https://www.youtube.com/watch?v=pzUBrJLIESU;License: Standard Youtube License
Lecture 1 - Propositional Logic; Author: nptelhrd;https://www.youtube.com/watch?v=xlUFkMKSB3Y;License: Standard YouTube License, CC-BY
MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY