al let (xt) betopology space and BCY then B is closed in y iff there is closed set CinX st B-COY
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- Ris not connected if T is * O None of the choices the trivial (usual) topology the indiscrete topology O the finite closed topology(X,ex) and (9,cy) be tus portially ordered sets bts set Xxy for each on Ca,b), (cid) E X x y laib)< (cid) o aLet P(A) be the power set of a non-empty set A A relation R on P(A) is defined as follows: R= {(X,Y): X CY} Example (1) reflexivity, (ii)symmetry and (i) transitivity of R on P(A).Prove that for subset X , Y, and Z of given universal set UDetermine whether these statements are true or false. Enter T or F. (a) Cardinality of {Ø} is 0. (b) {0}{0} (c) Ø C {0} (d) 0 € ØExample [2.1.21]| Let Ej and E, are subsets of a space X show that whether each one of the following statements true or fals and why? 1) (E, U E2)° = E,° U E,° ESE 2) (E, N E2)° = E,° n E,° (5,0E)S E,UE 3) (E, U E2)° = E,° U E,° 4) (E, N E2)º = E,° n E2° 5) d(E, U E2) = d(E,)U d(E2) 6) d(E, N E2) = d(E,)nd(E,) 7) (E U E2)' = E,' U E,' 8) (Ε η Ε) = E' n E. 9) (E, U E2) = E, U E, 10) (E, N E2) = E, N E, %3D***** FIVE STAR. ***** FIVE STAR. 8. Let X be a metric space. Let in X. Show either ESA or connected subset of A UB. proof. Let X be a metric space. Let A and B be seperated sets in X. ⇒ AnB = 8. A and B be seperated sets ECB where Eis a Let E → E & AUB. 3DF (BOF). However, AnB = ∞ so be the connected subset of AUB. s.t. DReal Analysis 1Tinio ishob Let a universe be given by (5) and suppose that subsets of U are A (1,5), B-12,5,3), C= (4,2). Find (a) AU(BUC) (b) (AUB)UC, (c) An(BC) U-(1,2,3,4,5) that subsets of U are A (1,5), B-12,5,3), C= and suppose 14.2). Find (a) AU(BUC) (b) (AUB)UC, (c) An(BuC) (d) (AnB)U(AnC)(e) A'n(B'nC) () (AUB) - (AUC). Let U be the set of all non negative integers and (6) consider the subsets. A Ixlx is an even integer, 1Sx<6) and B= (xlx is a prime number, 0Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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