(P Q). - Snistnote
... Ex: either P Q or Q P is included but not both. For two variables P and Q , there are 22 such formulas given by P Q, P ~ Q , ~ P Q and ~ P ~ Q these formulas are called minterms. ...
... Ex: either P Q or Q P is included but not both. For two variables P and Q , there are 22 such formulas given by P Q, P ~ Q , ~ P Q and ~ P ~ Q these formulas are called minterms. ...
Spelling / Vocabulary Words
... Define a variable and write an algebraic expression for each phrase: a. 9 less than a number b. The sum of twice a number and 31 c. The product of one half of a number and one third of the same number ...
... Define a variable and write an algebraic expression for each phrase: a. 9 less than a number b. The sum of twice a number and 31 c. The product of one half of a number and one third of the same number ...
Book Question Set #1: Ertel, Chapter 2: Propositional Logic
... d. ( A IMPLIES B ), where A and B are a propositional variable An implication that, ‘if A then B’ (also known as material implication) e. ( A EQUIVALENT-TO B ), where A and B are a propositional value A statement of equivalence where, ‘A if and only if B’ 6.) What does it mean for two propositional ...
... d. ( A IMPLIES B ), where A and B are a propositional variable An implication that, ‘if A then B’ (also known as material implication) e. ( A EQUIVALENT-TO B ), where A and B are a propositional value A statement of equivalence where, ‘A if and only if B’ 6.) What does it mean for two propositional ...
Logic Handout - EECS: www
... simple circuits (each with only a handful of transistors) that can be wired together to implement any CL function. In CS61c we consider logic gates are primitive elements; they are the basic building blocks for our circuits. Here are some common logic gates. For each we show its name, its graphical ...
... simple circuits (each with only a handful of transistors) that can be wired together to implement any CL function. In CS61c we consider logic gates are primitive elements; they are the basic building blocks for our circuits. Here are some common logic gates. For each we show its name, its graphical ...
What is a linear function of several independent
... Question 1: What is a linear function of several independent variables? In section 1.1, we introduced a linear function of one variable, y mx b . There was nothing special about the names of the variables, x and y, or the names of the constants, m and b. Another possible form for a linear functi ...
... Question 1: What is a linear function of several independent variables? In section 1.1, we introduced a linear function of one variable, y mx b . There was nothing special about the names of the variables, x and y, or the names of the constants, m and b. Another possible form for a linear functi ...
CPSC 2105 Lecture 6 - Edward Bosworth, Ph.D.
... The fact that any Boolean variable can assume only one of two possibly values can be shown, by induction, to imply the following. For N > 0, N Boolean variables can take only 2N different combinations of values. For small values of N, we can use this to specify a function using a truth table with 2N ...
... The fact that any Boolean variable can assume only one of two possibly values can be shown, by induction, to imply the following. For N > 0, N Boolean variables can take only 2N different combinations of values. For small values of N, we can use this to specify a function using a truth table with 2N ...
Exam 1
... a) Computers are commercially successful strictly due to their speed / cost b) Placing an entire processor on a single chip made computers much cheaper c) The number of transistors on a chip is twice as many now as there were 10 years ago d) The goal of the computer architect is to make it easy to p ...
... a) Computers are commercially successful strictly due to their speed / cost b) Placing an entire processor on a single chip made computers much cheaper c) The number of transistors on a chip is twice as many now as there were 10 years ago d) The goal of the computer architect is to make it easy to p ...
One and Two digit Addition and Subtraction - Perfect Math
... • A polynomial has multiple variables that we cannot add together, such as x and y, or x and x2 • We can actually have as many variables and exponents of variables as we can fit. • There are ways to add, subtract, multiply, and divide these still even if the variables do not add up. ...
... • A polynomial has multiple variables that we cannot add together, such as x and y, or x and x2 • We can actually have as many variables and exponents of variables as we can fit. • There are ways to add, subtract, multiply, and divide these still even if the variables do not add up. ...
BOOLEAN ALGEBRA AND LOGIC SIMPLIFICATION
... • When two or more sum terms are multiplied by Boolean multiplication, the result is a • Product-of-Sum or POS expression. • • (A + B)(A + B + C) • • (A + B + C)(C + D + E)(B + C + D) • • (A + B)(A + B + C)(A + C) • The Domain of a POS expression is the set of variables contained in the expression, ...
... • When two or more sum terms are multiplied by Boolean multiplication, the result is a • Product-of-Sum or POS expression. • • (A + B)(A + B + C) • • (A + B + C)(C + D + E)(B + C + D) • • (A + B)(A + B + C)(A + C) • The Domain of a POS expression is the set of variables contained in the expression, ...
notes 25 Algebra Variables and Expressions
... • ADV Practice pg.453 #1-15 ALL • REG Practice pg.453 #2-14 EVEN https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6thexpressions-and-variables/cc-6th-substitution/v/variables-andexpressions-1 https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6thexpressions-and-variables/cc-6th-substitut ...
... • ADV Practice pg.453 #1-15 ALL • REG Practice pg.453 #2-14 EVEN https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6thexpressions-and-variables/cc-6th-substitution/v/variables-andexpressions-1 https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6thexpressions-and-variables/cc-6th-substitut ...
functional model
... – The rows represent inputs and the corresponding outputs. – Columns are input and output variables. • It is the simplest way to represent a circuit. • In Boolean arithmetic, the possible values are 0 and 1. So for an ninput gate, number of possible outcomes = 2n • The inputs are given in an increme ...
... – The rows represent inputs and the corresponding outputs. – Columns are input and output variables. • It is the simplest way to represent a circuit. • In Boolean arithmetic, the possible values are 0 and 1. So for an ninput gate, number of possible outcomes = 2n • The inputs are given in an increme ...
Homework 3
... Problem 4: Consider a set K of numbers having all eight factors of 30, that is, {1, 2, 3, 5, 6, 10, 15, 30}. Let two binary operations be LCM (least common multiple) denoted as + and GCF (greatest common factor) denoted as · . Show that: (a) The identity element for + (LCM) is 1 and that for · (GCF) ...
... Problem 4: Consider a set K of numbers having all eight factors of 30, that is, {1, 2, 3, 5, 6, 10, 15, 30}. Let two binary operations be LCM (least common multiple) denoted as + and GCF (greatest common factor) denoted as · . Show that: (a) The identity element for + (LCM) is 1 and that for · (GCF) ...
CSE596, Fall 2015 Problem Set 1 Due Wed. Sept. 16
... (1) Design a deterministic finite automaton with alphabet {0, 1} to recognize the language of binary numbers (in standard binary notation with leading zeroes allowed) that are multiples of 5. It is your choice whether you prefer to include the empty string λ in this language, or not—you must state y ...
... (1) Design a deterministic finite automaton with alphabet {0, 1} to recognize the language of binary numbers (in standard binary notation with leading zeroes allowed) that are multiples of 5. It is your choice whether you prefer to include the empty string λ in this language, or not—you must state y ...
3.1 Review 3.2 The truth table method
... • Drop every clause containing p (why?: Ci evals to true, we don’t need it anymore) • Drop every ¬p from the remaining clauses (why?: if Cj evals to true, then it doesn’t have to do with ¬p, which is false) • The formula doesn’t contain p anymore Repeat splitting the remaining variables in the remai ...
... • Drop every clause containing p (why?: Ci evals to true, we don’t need it anymore) • Drop every ¬p from the remaining clauses (why?: if Cj evals to true, then it doesn’t have to do with ¬p, which is false) • The formula doesn’t contain p anymore Repeat splitting the remaining variables in the remai ...
Normal Forms
... Proof First construct an equivalent rectified formula. Then pull the quantifiers to the front using the following equivalences from left to right as long as possible: ¬∀x F ...
... Proof First construct an equivalent rectified formula. Then pull the quantifiers to the front using the following equivalences from left to right as long as possible: ¬∀x F ...
21. Solve by Elimination
... Combine the solved x value and the solved y value into an ordered pair to determine the solution for the system. ____________________. Example 2: ...
... Combine the solved x value and the solved y value into an ordered pair to determine the solution for the system. ____________________. Example 2: ...
Lecture Notes 2
... to contradiction”. To prove a proposition x it’s sufficient to assume the negation ¬x of x and deduce from ¬x two contradictory statements, say, y and ¬y. The the above tautology implies that x is true. Many mathematical theorems can be formally described by an implication x → y. Call this implication ...
... to contradiction”. To prove a proposition x it’s sufficient to assume the negation ¬x of x and deduce from ¬x two contradictory statements, say, y and ¬y. The the above tautology implies that x is true. Many mathematical theorems can be formally described by an implication x → y. Call this implication ...
EECS 203-1 – Winter 2002 Definitions review sheet
... it is true for all possible assignments of truth values to its variables. A contradictory expression is false for all assignments of truth values to its variables. A satisfiable formula is an expression which is true for at least one assignment. • Logical equivalence and implication in propositional ...
... it is true for all possible assignments of truth values to its variables. A contradictory expression is false for all assignments of truth values to its variables. A satisfiable formula is an expression which is true for at least one assignment. • Logical equivalence and implication in propositional ...
CS302midtermpaper
... 6. the diagram above shows the general implementation of ________ form * POS 7. The expression _________ is an example of Commutative Law for Multiplication. * AB=BA (Page 72) 8. Consider a circuit consisting of two consecutive NOT gates, the entire circuit belongs to a CMOS 5 Volt series, if certa ...
... 6. the diagram above shows the general implementation of ________ form * POS 7. The expression _________ is an example of Commutative Law for Multiplication. * AB=BA (Page 72) 8. Consider a circuit consisting of two consecutive NOT gates, the entire circuit belongs to a CMOS 5 Volt series, if certa ...