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Below, in the first three questions, A and B denote sets. (a) Prove or disprove, using any method, the following statement: P(A-B)| = 2|4|-|B| where P(X) is the power-set of X.

Below, in the first three questions, A and B denote sets. (a) Prove or disprove, using any method, the following statement: P(A-B)| = 2|4|-|B| where P(X) is the power-set of X.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 22E: A relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which...
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Please do (a) part only i need 200 percent exact answer so please solve according to question requirements in 30 min and get a thumb up
Below, in the first three questions, A and B denote sets. (a) Prove or disprove, using any method, the following statement: P(A-B)=214-B, where P(X) is the power-set of X. ATH2411 - Mathematics for Computing 1 Take Home Exercise (b) Prove that A (BA) = A - B using the set identities provided in Table 1.5.1 of ZyBooks as well as the set subtraction law: A - B = AnB. (c) Prove that A (BA) = A - B, but this time using definitions only (of sets, set operations, set relations, etc.), as per ZyBooks Section 3.8 (Chapter 8 in Book of Proofs). You should NOT use set identities. Prove by induction that for any positive integer n. 4 divides 32" - 1. Is the statement "If √13 & Q, then √25 & Q" True or False? Explain your answer in detail (proof something if necessary). You can use the fact that if n is an integer such that 13 divides n², then 13 divides n. (f) Given the following clauses: (d) (e) (-PVW) ^ (PVQVT)^(-S) A (PVQVS)^(-QVT)^(-T)^(-W) Perform the smallest possible resolution refutation, that is, prove the above CNF formula is unsatisfiable (i.e., a contradiction) in the smallest number of steps. Prove by resolution that KB = 0, where: KB=(-PVW) A (PVQVT)^(-S) A (PVQVS)^(-T)^(-W) and Ф= QA-T Provide a proof showing all the steps of your reasoning.
Transcribed Image Text:Below, in the first three questions, A and B denote sets. (a) Prove or disprove, using any method, the following statement: P(A-B)=214-B, where P(X) is the power-set of X. ATH2411 - Mathematics for Computing 1 Take Home Exercise (b) Prove that A (BA) = A - B using the set identities provided in Table 1.5.1 of ZyBooks as well as the set subtraction law: A - B = AnB. (c) Prove that A (BA) = A - B, but this time using definitions only (of sets, set operations, set relations, etc.), as per ZyBooks Section 3.8 (Chapter 8 in Book of Proofs). You should NOT use set identities. Prove by induction that for any positive integer n. 4 divides 32" - 1. Is the statement "If √13 & Q, then √25 & Q" True or False? Explain your answer in detail (proof something if necessary). You can use the fact that if n is an integer such that 13 divides n², then 13 divides n. (f) Given the following clauses: (d) (e) (-PVW) ^ (PVQVT)^(-S) A (PVQVS)^(-QVT)^(-T)^(-W) Perform the smallest possible resolution refutation, that is, prove the above CNF formula is unsatisfiable (i.e., a contradiction) in the smallest number of steps. Prove by resolution that KB = 0, where: KB=(-PVW) A (PVQVT)^(-S) A (PVQVS)^(-T)^(-W) and Ф= QA-T Provide a proof showing all the steps of your reasoning.
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