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CSCE 222 CSCE222 Final exam – Texas A&M

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CSCE 222 CSCE222 Final exam – Texas A&M

ab

True if both are true

ab

True if at least one is true

ab

True if only one is true

a → b

False if a is true and b is false

a ↔ b

True if a and b are both false or true

Tautology

Only if a truth table always evaluates to true

a ≡ b

Only logically equivalent if a and b are tautologies

Conditional“p →

Description

CSCE 222 CSCE222 Final exam – Texas A&M

ab

True if both are true

ab

True if at least one is true

ab

True if only one is true

a → b

False if a is true and b is false

a ↔ b

True if a and b are both false or true

Tautology

Only if a truth table always evaluates to true

a ≡ b

Only logically equivalent if a and b are tautologies

Conditional“p → q” “if p then q”

p is premise or hypothesis

q is conclusion or consequence

¬xP(x)

x¬P(x)

¬xP(x)

x¬P(x)

¬(pq)

¬p¬q

¬(pq)

¬p¬q

p → q ≡

¬pq

Modus Ponens

(p(p→ q)) → q

Modus Tollens

(¬q(pq))¬p

Simplification

pqp

Generating function and expansion of 1 / (1-x)

Sum from 0 to infinity of X^n = (1,1,1,1,1,1,1,1,…)

Generating function and expansion of 1 / (1-x)^2

Sum from 0 to infinity of (n+1)X^n = (1,2,3,4,…)

Practice some characteristic equations now.

Yes sir

CSCE 222 CSCE222 Final exam – Texas A&M

CSCE 222 Discrete Structures for Computing School: Texas A&M University (Texas A&M) *Professor:math, Lee, KLAPPENECKER, Klappenacker, n… Documents (404) Q&A (32) Textbook Exercises (20+)

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CSCE 222 CSCE222 Final exam – Texas A&M

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CSCE 222 – Spring 2014 Register Now hw7.pdf Textbook Exercises Discrete Mathematics and Its Applications image Discrete Mathematics and Its Applications Ch 1, Section 1.1 Propositional Logic, Exercise 1The given sentence is a preposition as it is declarative and states a fact.

CSCE 222 CSCE222 Final exam – Texas A&M

Truth value of the…Discrete Mathematics and Its Applications Ch 2, Section 2.1 Sets, Exercise 1The given set contains the values of x which are the solutions of the equation {{x}^{2}}=1 .Discrete Mathematics and Its

Applications Ch 3, Section 3.1 Algorithms, Exercise 1The first number in the series is assigned to the variable max . Then, the algorithm recursively…Discrete Mathematics and Its Applications Ch 4, Section 4.1

Divisibility and Modular Arithmetic , Exercise 1A nonzero integer a divides another integer b if \dfrac{b}{a} results in an integer. Clearly,…Discrete Mathematics and Its Applications Ch 5, Section 5.1 Mathematical Induction , Exercise 1Let P\left( n \right) be “Vehicle T stops at a station n “.

Basis step: According to the…Discrete Mathematics and Its Applications Ch 6, Section 6.1 The Basics of Counting, Exercise 1Find the number of ways in which one representative can be picked from 18 M majors.

CSCE 222 CSCE222 Final exam – Texas A&M

Use the product…Discrete Mathematics and Its Applications Ch 7, Section 7.1 An Introduction to Discrete Probability , Exercise 1Use the Laplace’s definition of probability for an event.Discrete Mathematics and Its Applications Ch 8, Section 8.1 Applications of Recurrence Relations , Exercise 1Let P\left( n \right) be {{H}_{n}}={{2}^{n}}-1 .

Show that it is true for n=1 . When it is only one…Discrete Mathematics and Its Applications Ch 9, Section 9.1 Relations and Their Properties , Exercise 1Define the relation R=\left\{ \left( a,b \right)|a=b \right\} . The elements common to both the…

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CSCE 222 CSCE222 Final exam – Texas A&M

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