For Exercises 35–48, identity p, q, and r if necessary. Then translate each argument to symbols and use a truth table to decide if the argument is valid or invalid.
39. I will go to the party if and only if my ex-boyfriend is not going.
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- 1.2.6. (-) In the graph below (the paw), find all the maximal paths, maximal cliques, and maximal independent sets. Also find all the maximum paths, maximum cliques, and maximum independent sets.arrow_forward18 Find the expected value E(X) and the variance V(X) for the following probability density function. f(x)=2x-4 for 1arrow_forward1.2.13. Alternative proofs that every u, v-walk contains a u, v-path (Lemma 1.2.5). a) (ordinary induction) Given that every walk of length 1-1 contains a path from its first vertex to its last, prove that every walk of length / also satisfies this. b) (extremality) Given a u, v-walk W, consider a shortest u, u-walk contained in W.arrow_forward1.2.10. (-) Prove or disprove: a) Every Eulerian bipartite graph has an even number of edges. b) Every Eulerian simple graph with an even number of vertices has an even num- ber of edges.arrow_forward1) Calculate 49(B-1)2+7B−1AT+7ATB−1+(AT)2 2)Find a matrix C such that (B − 2C)-1=A 3) Find a non-diagonal matrix E ̸= B such that det(AB) = det(AE)arrow_forward1.2.4. (-) Let G be a graph. For v € V(G) and e = E(G), describe the adjacency and incidence matrices of G-v and G-e in terms of the corresponding matrices for G.arrow_forward1.2.6. (-) In the graph below (the paw), find all the maximal paths, maximal cliques, and maximal independent sets. Also find all the maximum paths, maximum cliques, and maximum independent sets.arrow_forward@if {fx. KG A} is collection of Countin uous function on a to Polgical Which separates Points Srem closed set then the toplogy onx is the weak toplogy induced by the Map fx. Prove that using dief speParts Point 1 B closed and x&B in X then Sor some kεA fx (X) fx (B). + spacearrow_forward1.2.9. (-) What is the minimum number of trails needed to decompose the Petersen graph? Is there a decomposition into this many trails using only paths?arrow_forwardYou are planning an experiment to determine the effect of the brand of gasoline and the weight of a car on gas mileage measured in miles per gallon. You will use a single test car, adding weights so that its total weight is 3000, 3500, or 4000 pounds. The car will drive on a test track at each weight using each of Amoco, Marathon, and Speedway gasoline. Which is the best way to organize the study? Start with 3000 pounds and Amoco and run the car on the test track. Then do 3500 and 4000 pounds. Change to Marathon and go through the three weights in order. Then change to Speedway and do the three weights in order once more. Start with 3000 pounds and Amoco and run the car on the test track. Then change to Marathon and then to Speedway without changing the weight. Then add weights to get 3500 pounds and go through the three gasolines in the same order.Then change to 4000 pounds and do the three gasolines in order again. Choose a gasoline at random, and run the car with this gasoline at…arrow_forward1.2.7. (-) Prove that a bipartite graph has a unique bipartition (except for interchang- ing the two partite sets) if and only if it is connected.arrow_forwardSx. KG A3 is collection of Countin uous function on a to Polgical Which separates Points Srem closed set then the toplogy onx is the weak toplogy induced by the map fx. Prove that using dief speParts Point If B closed and x&B in X then for some xеA fx(x) € fa(B). If (π Xx, prodect) is prodect space KEA S Prove s. BxXx (πh Bx) ≤ πTx B x Prove is an A is finte = (πT. Bx) = πT. Bå KEA XEAarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell