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2.1. Complete each statement. In (a) to (e), each letter, such as C, D, or R, represents a set or group. (a) If A is B and B is H, then _____ . (b) If C is D and P is C, then _____ . (c) If _____ and B is R, then B is S. (d) If E is F, F is G, and G is K, then _____ . (e) If G is H, H is R, and _____ , then A is R. (f) If triangles are polygons and polygons are geometric figures, then _____ . (g) If a rectangle is a parallelogram and a parallelogram is a quadrilateral, then _____ . 2.2. State the conclusions which follow when Postulate 1 is applied to the given data, which refer to Fig. 2-29. (2.2)



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(2.3)

Note!

Fig. 2-29

h e (2.4)

(b) Evaluate x 4y when x (c) Does b2 8 (d) Find x if x (e) Find y if x y y 17 when b 20 and y 20 and y

2.4. State the conclusions that follow when Postulate 3 is applied to the data in Fig. 2-30(a) and (b).

(2.5)

Fig. 2-30

The two most widely used methods of calculating interest are the cancellation method and the 6 per cent, 60-days method.

2.5. State a conclusion involving two new equals that follows when Postulate 4, 5, or 6 is applied to the given data. (2.6) (a) Given: b (b) Given: b e (Fig. 2-31). c, a d (Fig. 2-31).

(c) Given: j 4 > j 5 (Fig. 2-32). (d) Given: j 1 > j 3, j 2 > j 4 (Fig. 2-32).





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The DigestMethod element is required, and it identi es the digest algorithm to be applied to the signed object. The DigestValue is the element that contains the encoded value of the digest and is always encoded using base64. The SignatureValue element contains the actual value of the digital signature, and it is encoded according to the identi er speci ed in SignatureMethod. The KeyInfo element is optional and enables the recipient to obtain the key (or keys) needed to validate a signature. The KeyInfo element may contain keys, names, certi cates, and other public key management information, such as key distribution or key agreement data. If KeyInfo is left out, one is expected to be able to identify the key based on application context information. In the case of envelope signatures, it is the Object element that contains the object being signed. The digest is calculated over the entire Object element, including its Object tags. Object is an optional element that may occur one or more times. Let s look at a sample Signature element that contains data. This is from the XML-Signature Candidate Recommendation: <Signature Id="MySignatureExample" xmlns="http://www.w3.org/2000/09/xmldsig#"> This markup states that the signature has an ID, MySignatureExample, and is part of the namespace found at the stated URI. It is closed in the last line of the following example: <SignedInfo> <CanonicalizationMethod Algorithm="http://www.w3.org/TR/2000/CR-xml-c14n20001026"/> <SignatureMethod Algorithm="http://www.w3.org/2000/09/xmldsig#dsasha1"/> <Reference URI="http://www.w3.org/TR/2000/REC-xhtml120000126/"> <Transforms> <Transform Algorithm="http://www.w3.org/TR/2000/CR-xmlc14n-20001026"/> </Transforms> <DigestMethod Algorithm="http://www.w3.org/2000/09/ xmldsig#sha1"/> <DigestValue>j6lwx3rvEPO0vKtMup4NbeVu8nk= </DigestValue> </Reference> </SignedInfo>

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Fig. 2-31

Fig. 2-32

2.6. In Fig. 2-33 AD and BC are trisected (divided into 3 equal parts).

(2.7)

Fig. 2-33

A promissory note is a note payable from the standpoint of the maker; it is a note receivable from the standpoint of the payee. Notes Payable A note payable is a written promise to pay a creditor an amount of mon ey in the future. Notes are used by a business to purchase items, settle an open account, or borrow money from a bank. 1. Purchase items Assume that Spencer bought of ce equipment costing $2,000 by giving a note.

(a) If AD > BC, why is AE > BF (b) If EG > FH, why is AG > BH (c) If GD > HC, why is AD > BC (d) If ED > FC, why is EG > FH 2.7. In Fig. 2-34 j BCD and j ADC are trisected. (a) If mj BCD (b) If mj 1 mj ADC, why does mj FCD mj FDC

Fig. 2-34

(2.8)

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