Statements and negations - NIU
The negation of a for all statement is a some statement Example 6 The negation of All birds can y is Some birds cannot y The negation of a some statement is a for all statement Example 7 The negation of There exists an honest man is All men are dishonest Example 8 Consider the statement All numbers can be factored
PART 2 MODULE 1 LOGIC: STATEMENTS, NEGATIONS, QUANTIFIERS
The negation of "Some A are B" is "No A are (is) B " (Note: this can also be phrased "All A are the opposite of B," although this construction sometimes sounds ambiguous ) EXAMPLE 2 1 2 Write the negation of "Some used cars are reliable " Fact: "Some aren't" is the opposite of "all are "
02 Quantifiers and Negation - Cornell University
0 2 Quantiflers and Negation 1 0 2 Quantifiers and Negation Interesting mathematical statements are seldom like \2 + 2 = 4"; more typical is the statement \every prime number such that if you divide it by 4 you have a remainder of 1 is the sum of two squares " In other words, most interesting
Math 127: Propositional Logic
2 3 Negation Our last basic logical operator is negation, a fancy way to say ot " De nition 5 Let p be a proposition The negation of p, denoted :p, is a proposition that is true when p is false, and false when p is true This operator is fairly straightforward: it simply takes the opposite truth value from p A truth table for :p takes the
Discrete Mathematics, Chapter 11-13: Propositional Logic
negation 2 Push negations inward by De Morgan’s laws and the double negation law until negations appear only in literals 3 Use the commutative, associative and distributive laws to obtain the correct form 4 Simplify with domination, identity, idempotent, and negation laws (A similar construction can be done to transform formulae into
Truth Tables for Negation, Conjunction, and Disjunction
Title: Microsoft PowerPoint - lec3_2_3 ppt Author: Revathi Created Date: 10/4/2005 7:25:01 PM
Predicates and Quantifiers - Rutgers University
Distributing a negation operator across a quantifier changes a universal to an existential and vice versa Multiple Quantifiers: read left to right _____ Example: Let U = R, the real numbers, P(x,y): xy= 0 ∀ x∀ yP (x,y) ∀ x∃ yP (x,y) ∃ x∀ yP (x,y) ∃ x∃ yP (x,y) The only one that is false is the first one
p implies q p q p premise q conclusion Example 1
the negation of an implication is an and statement The negation of the statement pimplies q is the statement pand not q: 4 Example 5 (1) The negation of
Discrete Mathematics for Computer Science
Negation • Negate the following propositions: – It is raining today • It is not raining today – 2 is a prime number •2 i s not a prime number – There are other life forms on other planets in the universe • It is not the case that there are other life forms on other planets in the universe CS 441 Discrete mathematics for CS M
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