11+12 Mathematical Statements & Universal true for all Gcommon phrase elements in a set Por all 2. Conditional thing B Eme thing a true, then oferes Ras to be true common phrase: If-then 3. Existential at least one thin thing is true. Commen porase there is of there oxists. 4. Moiversal-conditional Eg for all animals a, If a dog, then mammal. So Universal-existentials Gfirst prost True serind paret assorts Eg for all real additive of something. nas, there exists As inverwe aw axistence 6. Existential-Universal 8- first part arserts that a second part says object satisfies for all things of certain dijest exists. a certain property a xestrin kind eg. There Is a equal جه Integer that ju less than every positive integers. LAGUAGE DE SETS ZES xis an element of s Gx is not element of s Set with just one elementy what represente Imp {1, 2}} G toc elements how many elements? As set of all real nous set of all integers 9 set of all integers erational nois, or quotients of Set of real noos is divided Pato is poorts 1. set of tve real noa 2. set of -ve real no. 3. number 0. →O is neither tve nor -ve not edd. 4 But o is even, *Set-Builder Notation XES IP Gset of all elements x in set s such that P(x) is true + Subsets GACB [A s for all elements A subset PBB] x, if xe A than REB Deductive reasoning & process of reasoning ferous one or more greach a Statements (premises) to logically certain conduion. * sirgument is a sequence of statements aimed at demonstrating the truth of an axertione Statements 35 It is sentence that is true en false but not both.. sentence it is wethen for some instaure Some instances. the sentence cau true and also false for COMPOUND STATEMENTS 2 & not & negatron A and & conjunction or : disjunction order of operations & x<3 r&x=3 a) x=3 qvr b) 02 x <3 Blqr) TRUTH VALUES NEGATION (not) CONJUNCTION (and) True, when bate are true False if Eme of thour or boter are false DISJUNCTION (os) True, when one of them of both are true fabe, when both are falre → Logical Equivalence → De morgan's law & ~(p^2) = ~p vng ~Bvq) = up ^ Ng →Toutology →Contradiction Galway's TRUE Galways FALSE Imp: If it is tavology show that pat and is contradiction, and game truth values, Same truse Tolios, pnt = p prcc → simplifying statement forms CONDITIONAL STATEMENTS ← If B then g f hypothesis | antecedent 9 condusion I consequient false, when True B is T, q is f otherwise

Lesson 1: Mathematical Statements

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