![4. [7 marks] Choosing a universe and predicates. (a) Consider the following statement: Vx EN, P(r, 165)P(x,1) Provide one definition of a binary predicate P over Nx N that makes the above statement True, and another definition of P that makes the statement False. Briefly justify your answers, but no formal proofs are necessary b) Consider the following statement: Provide one definition of a non-empty set U, and predicates P, Q, and R over U, that makes the above statement True, and another definition definition of a non-empty set U, and predicates P, Q, and R that makes the statement False. Briefly justify your answers, but no formal proofs are necessary](http://img.homeworklib.com/questions/82039f60-6fe4-11ea-9389-99832382268f.png?x-oss-process=image/resize,w_560)
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4. [7 marks] Choosing a universe and predicates. (a) Consider the following statement: Vx EN, P(r,...
Provide complete definitions for the following: 7 marks] Choosing a universe and predicates. (a) Consider the...
Provide complete definitions for the following:
7 marks] Choosing a universe and predicates. (a) Consider the following statement: Vz E N, P(x,165) -> P(x, 1) Provide one definition of a binary predicate P over N x N that makes the above statement True, and another definition of P that makes the statement False. Briefly justify your answers, but no formal proofs are necessary. b) Consider the following statement: Provide one definition of a non-empty set U, and predicates P, Q,...
Consider the following statement Provide one definition of a non-empty set U, and predicates P, Q, and R over U, that m...
Consider the following statement Provide one definition of a non-empty set U, and predicates P, Q, and R over U, that makes the above statement true, and another definition of a non-empty set U, and predicates P, Q, and R that makes the statement false. Briefly justify your answers, but no formal proofs are necessary.
Consider the following statement Provide one definition of a non-empty set U, and predicates P, Q, and R over U, that makes the above statement...
5. Symbolize the following argument and prove it is a valid argument. Let B ( x...
5. Symbolize the following argument and prove it is a valid argument. Let B ( x ) = x is a bear; D ( x ) = x is dangerous, and H ( x ) = x is hungry. Every bear that is hungry is dangerous. There is a hungry animal that is not dangerous. Therefore there is an animal that is not a bear. 6. In order to prove an quantificational argument invalid it is only necessary to find a...
2. 9 marks] Strings. Consider the following definitions on strings Let U be the set of all strings Let s be a str...
2. 9 marks] Strings. Consider the following definitions on strings Let U be the set of all strings Let s be a string. The length or size of a string, denoted Is, is the number of characters in s Let s be a string, and i e N such that 0 < ί < sl. We write s[i] to represent the character of s at index i, where indexing starts at 0 (so s 0] is the first character, and...
2. 9 marks] Strings. Consider the following definitions on strings Let U be the set of all strings. Let s be a stri...
2. 9 marks] Strings. Consider the following definitions on strings Let U be the set of all strings. Let s be a string. The length or size of a string, denoted Is, is the number of characters in s Let s be a string, and ie N such that 0 Si< Is. We write si] to represent the character of s at index i, where indexing starts at 0 (so s(0 is the first character, and s|s -1 is the...
4.The (p,q) hypergeometric function is defined as where aj ∈ R, bl ∈ R and for...
4.The (p,q) hypergeometric function is defined as where aj ∈ R, bl ∈ R and for any real value a we have that (a)0 =1 (a)n =a(a + 1)(a + 2)···(a + n − 1), n ≥ 1. So for example, we have that 0F0(;;x) = ex, and if we have the Bessel function Jn(x) where , then we have . Write a program which computes the (p,q) hypergeometric function. It should take as input vectors a and b where...
#7. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) k in Z k2 + 9 = 0....
#7. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) k in Z k2 + 9 = 0. ________(b) m, n in N, 5m 2n is in N. ________(c) x in R, if |x − 2| < 3, then |x| < 5. #8. For each statement, (i) write the statement in logical form with appropriate variables and quantifiers, (ii) write the negation in logical form, and (iii) write the negation in a clearly worded unambiguous English sentence....
3. Let W = P({1,2,3,4,5}). Consider the following statement and attempted proof: VAE W WB EW...
3. Let W = P({1,2,3,4,5}). Consider the following statement and attempted proof: VAE W WB EW (((AUB) C A) + (ACB)) (1) Towards a universal generalization argument, choose arbitrary A € W, BEW. (2) We need to show ((AUB) C A) + (ACB). (3) Towards a proof by contraposition, assume B CA, and we need to show A C (AUB). (4) By definition of subset inclusion, this means we need to show Vc (E A →r (AUB)). (5) Towards a...
Hi, could you post solutions to the following questions. Thanks. 2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 sta...
Hi,
could you post solutions to the following questions. Thanks.
2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 state whether they are subepaces of R3 or not by clearly explaining your answer. 2% 2% (c) Consider the map F : R2 → R3 defined by for any z = (zi,Z2) E R2. 3% 3% 3% 3% i. Show that...
Need help with stats true or false questions Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% con...
Need help with stats true or false questions
Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% confidence interval for A In this case, a t-test with significance level 1% rejects the null hypothesis Ho : A-0 against a two sided alternative. b) Complicated models with a lot of parameters are better for prediction then simple models with just a few parameters c)...
Provide complete definitions for the following:
7 marks] Choosing a universe and predicates. (a) Consider the following statement: Vz E N, P(x,165) -> P(x, 1) Provide one definition of a binary predicate P over N x N that makes the above statement True, and another definition of P that makes the statement False. Briefly justify your answers, but no formal proofs are necessary. b) Consider the following statement: Provide one definition of a non-empty set U, and predicates P, Q,...
Consider the following statement Provide one definition of a non-empty set U, and predicates P, Q, and R over U, that makes the above statement true, and another definition of a non-empty set U, and predicates P, Q, and R that makes the statement false. Briefly justify your answers, but no formal proofs are necessary.
Consider the following statement Provide one definition of a non-empty set U, and predicates P, Q, and R over U, that makes the above statement...
2. 9 marks] Strings. Consider the following definitions on strings Let U be the set of all strings Let s be a string. The length or size of a string, denoted Is, is the number of characters in s Let s be a string, and i e N such that 0 < ί < sl. We write s[i] to represent the character of s at index i, where indexing starts at 0 (so s 0] is the first character, and...
2. 9 marks] Strings. Consider the following definitions on strings Let U be the set of all strings. Let s be a string. The length or size of a string, denoted Is, is the number of characters in s Let s be a string, and ie N such that 0 Si< Is. We write si] to represent the character of s at index i, where indexing starts at 0 (so s(0 is the first character, and s|s -1 is the...
3. Let W = P({1,2,3,4,5}). Consider the following statement and attempted proof: VAE W WB EW (((AUB) C A) + (ACB)) (1) Towards a universal generalization argument, choose arbitrary A € W, BEW. (2) We need to show ((AUB) C A) + (ACB). (3) Towards a proof by contraposition, assume B CA, and we need to show A C (AUB). (4) By definition of subset inclusion, this means we need to show Vc (E A →r (AUB)). (5) Towards a...
Hi,
could you post solutions to the following questions. Thanks.
2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 state whether they are subepaces of R3 or not by clearly explaining your answer. 2% 2% (c) Consider the map F : R2 → R3 defined by for any z = (zi,Z2) E R2. 3% 3% 3% 3% i. Show that...
Need help with stats true or false questions
Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% confidence interval for A In this case, a t-test with significance level 1% rejects the null hypothesis Ho : A-0 against a two sided alternative. b) Complicated models with a lot of parameters are better for prediction then simple models with just a few parameters c)...
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