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3.1.7 Remark. Trivially, for any R:A → B, we have dom(R) C A and ran(R) CB...
1. For any triangle ABC, we have a = b cos C +c cos B. Use...
1. For any triangle ABC, we have a = b cos C +c cos B. Use (i) the Law of Sines and (ii) the extended Law of Sines to deduce the addition formula: sin(B+C) = sin B cos C+ cos B sin C. (Hint: There will be 2 types of proof, i.e. by (i) and by (ii))
11) Assume that for an infinite family of events (Ann1 we have that AntI C An...
11) Assume that for an infinite family of events (Ann1 we have that AntI C An for any neN and that Show that 1 of 1 you don't have to give a rigorous topological proof. P(A)lm (A) -+00 r prokm
Advanced Calculus-2 proof: Suppose that we have two numbers a,b belong to R with a<=b. Suppose...
Advanced Calculus-2 proof: Suppose that we have two numbers a,b belong to R with a<=b. Suppose we have a continuous function f : [a,b] -> R. Then there are two numbers c,d belong to R with c<=d such that f([a,b]) = [c,d].
Prove/Justify. help plz. Remark 8.46. The following facts are easily verified. (a) (A) is the intersection of all ideals containing A. (b) If R is commutative, then (a)-aR :-|ar l r є R. Example 8.47...
Prove/Justify. help plz.
Remark 8.46. The following facts are easily verified. (a) (A) is the intersection of all ideals containing A. (b) If R is commutative, then (a)-aR :-|ar l r є R. Example 8.47. In Z, nZ = (n) = (-n). In fact, these are the only ideals in Z (since these are the only subgroups). So, all the ideals in Z are principal. If m and n are positive integers, then nZ C mZ if and only if...
Question 3. Given the relation Ron A = {a,b,c,d,e) by the pairs R = {(a,b), (cb),...
Question 3. Given the relation Ron A = {a,b,c,d,e) by the pairs R = {(a,b), (cb), (b, d), (e,d)} (a) (2 MARKS) Display the transitive closure R+ of R as a set of pairs. (b) (1 MARK) Explain why R+ is an order. Caution: An order has two defining properties. (c) (2 MARKS) Display the Hasse diagram of the order R+ (d) (1 MARK) Display the set of minimal members of R+.
positive, then r +y> V+y 10. If r and y are (a) Quantify this statement. (b)...
positive, then r +y> V+y 10. If r and y are (a) Quantify this statement. (b) Give a careful proof of this statement. (c) Suppose drop the condition that r andy be positive, but add the absolute value: we Show that this proposition is false. (d) What if we are more careful and write Jrl + lyl> Vr2 +y2. Is this now true? 11. Consider the statement: The sum of V2 and a rational number is irrational. (a) How should...
Let A = ( a, b, c, d ) and let ( A, R ) be a posset where R is a Relation on A defined by: ...
Let A = ( a, b, c, d ) and let ( A, R ) be a posset where R is a Relation on A defined by: R is reflexive c ≤ d a ≤ c a ≤ b a ≤ d b ≤ d Find H(A) Is (A, R) a lattice? If you answer no, give a counterexample. If you answer yes, give a brief justification as to why (no formal proof needed). Is (A,R) a Boolean algebra? Give...
5. If P(AB)-1, show that P(B (i) P(A n B n C) (ii) P(C|A B)-P(CB); and...
5. If P(AB)-1, show that P(B (i) P(A n B n C) (ii) P(C|A B)-P(CB); and n C) for any event C (iii) P(A n CB) P(CB).
HW4 7-4. Suppose that samples of size n=25 are selected at ran- dom from a normal...
HW4 7-4. Suppose that samples of size n=25 are selected at ran- dom from a normal population with mean 100 and standard deviation 10. What is the probability that the sample mean falls in the interval from uly-1.70 touy +1.50 ? 7-5. A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 520 KN/m and standard deviation 25 KN/mp. Find the probability that a ran- dom sample of n= 6 fiber specimens will have...
Looking for full solutions of question （a）（b）and（c） Problem 4. Let A CR. Given any a, b...
Looking for full solutions of question （a）（b）and（c）
Problem 4. Let A CR. Given any a, b € R, with a <b, define (a,b) A = {2 € A:a < x <b}. We call (a, b) A an open interval in A (or an open interval relative to A). a) Show that (a, b) A = (a,b) n A. b) Prove that a set V C A is relatively open in A if and only if for every 3 EV, there...
1. For any triangle ABC, we have a = b cos C +c cos B. Use (i) the Law of Sines and (ii) the extended Law of Sines to deduce the addition formula: sin(B+C) = sin B cos C+ cos B sin C. (Hint: There will be 2 types of proof, i.e. by (i) and by (ii))
11) Assume that for an infinite family of events (Ann1 we have that AntI C An for any neN and that Show that 1 of 1 you don't have to give a rigorous topological proof. P(A)lm (A) -+00 r prokm
Prove/Justify. help plz.
Remark 8.46. The following facts are easily verified. (a) (A) is the intersection of all ideals containing A. (b) If R is commutative, then (a)-aR :-|ar l r є R. Example 8.47. In Z, nZ = (n) = (-n). In fact, these are the only ideals in Z (since these are the only subgroups). So, all the ideals in Z are principal. If m and n are positive integers, then nZ C mZ if and only if...
Question 3. Given the relation Ron A = {a,b,c,d,e) by the pairs R = {(a,b), (cb), (b, d), (e,d)} (a) (2 MARKS) Display the transitive closure R+ of R as a set of pairs. (b) (1 MARK) Explain why R+ is an order. Caution: An order has two defining properties. (c) (2 MARKS) Display the Hasse diagram of the order R+ (d) (1 MARK) Display the set of minimal members of R+.
positive, then r +y> V+y 10. If r and y are (a) Quantify this statement. (b) Give a careful proof of this statement. (c) Suppose drop the condition that r andy be positive, but add the absolute value: we Show that this proposition is false. (d) What if we are more careful and write Jrl + lyl> Vr2 +y2. Is this now true? 11. Consider the statement: The sum of V2 and a rational number is irrational. (a) How should...
5. If P(AB)-1, show that P(B (i) P(A n B n C) (ii) P(C|A B)-P(CB); and n C) for any event C (iii) P(A n CB) P(CB).
HW4 7-4. Suppose that samples of size n=25 are selected at ran- dom from a normal population with mean 100 and standard deviation 10. What is the probability that the sample mean falls in the interval from uly-1.70 touy +1.50 ? 7-5. A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 520 KN/m and standard deviation 25 KN/mp. Find the probability that a ran- dom sample of n= 6 fiber specimens will have...
Looking for full solutions of question （a）（b）and（c）
Problem 4. Let A CR. Given any a, b € R, with a <b, define (a,b) A = {2 € A:a < x <b}. We call (a, b) A an open interval in A (or an open interval relative to A). a) Show that (a, b) A = (a,b) n A. b) Prove that a set V C A is relatively open in A if and only if for every 3 EV, there...
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