MATH 211 Exam 2, Spring 2008

AMERICAN UNIVERSITY OF BEIRUT 3 Math 211- Spring 2007 ; Drop Quiz.2, section 1, March 8, 2007 “AUB ID number: 200.0000 leccteee “Section: ....4., - — i, pb _ Question 1: Let p be the proposition: . : { 'Z “There is a student in this class who has taken every mathematics course offered at this schoo!” a) Express Pp using quantifiers and predicate: Lis AL Qhvclouts Vn tig clare . Co AL weet courtes: &, aot Luin aches : PCa ay \ Stuctsnt a. thas tal cw rd. 4 x Yq PG«.y\ b)_ Express the negation of p using quantifiers and predicate, and so that the negation symbol immediately precede the predicate: (axV¢4 PCw <B) Ndaco7 (v4. is c) Express the negation of p in English: For eve Stuclank i kbs CQouas there +s @ quathemebcs course Rak dlls atuckuk las not taken. ay — \~ Question 2: Rewrite the following statement so that negations appear only within predicates (that is, so that no negation is outside a quantifier or an expression involving logical connectives): ; aVxdy (P(x, y) ASzR(x,y,2)) = eT 34( ) = Boe ¥4 “(Pld nagReap ) Y) Sax van Pac) v (33 Rcmesst)) vy, = Bx Vy (1 Peed Vo YR WREcud) Ve Question 3: Express each of these statements into logical expressions using predicates, quantifiers and logical connectives if necessary: : - a) Every user has access to exactly one mailbox: ; Li. all usecs . 4 MO ath wcatl owed " Plum) + fuser a Las acess tp willow m Yu tam (2e.m9 An (nti i> 1BGus)) \.b) There is a student in this class who has been in every room of at least one building on campus: D atl students in tte Jaw Br all boildinge oa cam pos Aa. Ab ¥ ~ (Ql) > P(4,%)) Rynoall wooms Son Cann pid Pls, v)s Shudeab 's has lain to room U QOS: aor ua din lout (ae'ng bes \. ¢). Some student in this class grew up in the same town with exactly one other student in this class: SKM ghydadts oon tu clan oo G Gey) © studaata 2 aud qu vp wo Te Ree toon. J tae) A VR (Gl=a) v GCy,d> &=9 va=9] we Q rv Oke dea 7 ca - : . Og, 5 To aU beg ag (oo eee oes ssissssssessssss Yo dudy (x4 1 Poxet) Schaal iva ae OP LEN boon t ; tx dg de Gare. Pl Ey APCy LK YRC Re, th >. Geax) v(3> »)| —