Homework Answers
(a) (∀x)B(x)→[R(x)]
(b) (∃x)B(x)∧~[S(x)]
(c) (∀x)S(x)→[R(x)]
(d) (∃x)B(x)∧~[R(x)]
(e) ∀x,(B(x)∧R(x))∧(∀x,(B(x)∧S(x))→R(x))
(f) ∀x,(B(x)∧R(x))→(B(x)∧S(x))
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Discrete math structures
Using the predicate symbols shown and appropriate quantifiers, write each English language statement...
a) Provide counterexamples to the following statements. i) a and b are integers where alb and...
a) Provide counterexamples to the following statements. i) a and b are integers where alb and bla, then a = b. ii) If n >0 then n>0. iii) If n is an even number, then n² + 1 is prime. iv) If n is a positive integer, then nº >n! b) Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.) B(x): x is a ball R(x):...
Given Statement: Some popular bands are overrated. P = is popular Key of Predicate Symbols and...
Given Statement: Some popular bands are overrated. P = is popular Key of Predicate Symbols and Individual Constants: B = is a band 0 = is overrated Which expression is the best translation of the given statement above into predicate logic? (3x)(PxBx) (x)0x (3x)[(PxBx) • Ox] (3x)(PBX Ox) (x)[(Px > Bx) • Ox] Given Statement: Key of Predicate Symbols and Individual Constants: All citizens have a right to life, liberty, and the pursuit of happiness. C = is a citizen...
1. Write each of the statements using variables and quantifiers: a) Some integers are perfect squ...
1. Write each of the statements using variables and quantifiers: a) Some integers are perfect squares. b) Every rational number is a real number. 2. Let P(x) = "x has shoes", Q(x) = "x has a shirt", and R(x,y) = "x is served by y". The universe of x is people. Rewrite the following predicates in words: a) ∀x∃y [(¬P(x) ∧ Q(x)) ⇒ ¬R(x,y)] b) ∃x∃y [(¬P(x) ∧ Q(x)) ∧ R(x,y)] c) P("Bill" ) ∨ (Q("Jim") ∧ ¬Q("Bill")) ⇒ R("Bill","Jim")
Do the following 3 things respectively with each of the two sentences given below 1. Translate it by using the defined predicate symbols and a quantifier 2. Transform it into an equivalent statement...
Do the following 3 things respectively with each of the two sentences given below 1. Translate it by using the defined predicate symbols and a quantifier 2. Transform it into an equivalent statement with a quantifier different from the one used in the lst translation (by applying QN); and 3. Articulate the corresponding sentence of the 2nd translation in ordinary English 5 15 Not all dogs bark. D: being a dog B: barking (SJ16] All philosophers are neither impractical nor...
16 pts) #4. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) A statement...
16 pts) #4. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) A statement is a sentence that is true. ________(b) In logic, p q refers to the "inclusive or, " true when either p or q or both are true. ________(c) The phrase "not p and not q" means "not both p and q." ________(d) The conditional statement p q is true if p is false. ________(e) The negation of p q is p ~q. #5....
CSCI/MATH 2112 Discrete Structures I Assignment 1. Due on Friday, January 18, 11:00 pm (1) Write...
CSCI/MATH 2112 Discrete Structures I Assignment 1. Due on Friday, January 18, 11:00 pm (1) Write symbolic expression for each of the statements below; then work out their negations; finally expressing each as complete sentence in English: (a) Roses are red, violets are blue. (b) The bus is late or my watch is slow. (c) If a number is prime then it is odd or it is 2. (d) If a number x is a prime, then (root ) x...
#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....
EXERCISES 4.2.5. Using the given symbolization key, translate each English-language asser tion in...
please help
EXERCISES 4.2.5. Using the given symbolization key, translate each English-language asser tion into First-Order Logic u: The set of all animals. D: The set of all dogs. S: The set of all animals who like to swim f: Fergis b: Bertie e: Emerson r L y: s is larger than y. 1) Bertie is a dog who likes to swim 2) Bertie, Emerson, and Fergis are all dogs. 3) Emerson is larger than Bertie, and Fergis is larger...
I need help on the blue highlighted questions and 20 from the last picture. Our professor...
I need help on the blue highlighted questions and 20 from the
last picture. Our professor doesn’t want a truth table. He wants a
proof.
In Exercises 13-24, use propositional logic to prove that the argument is valid. 13. (A VB')' A(BC) → (A' AC) 14. A' A( B A) →B' 15. (A →B) A [A → ( B C)] → ( AC ) 16.[( CD) →→[( CD) →D] 17. A' (A VB) →B Section 1.2 Propositional Logic 18. (A...
Using the book, write another paragraph or two: write 170 words: Q: Compare the assumptions of...
Using the book, write another paragraph or two: write 170
words:
Q: Compare the assumptions of physician-centered and
collaborative communication. How is the caregiver’s role different
in each model? How is the patient’s role different?
Answer: Physical-centered communication involves the specialists
taking control of the conversation. They decide on the topics of
discussion and when to end the process. The patient responds to the
issues raised by the caregiver and acts accordingly. On the other
hand, Collaborative communication involves a...
a) Provide counterexamples to the following statements. i) a and b are integers where alb and bla, then a = b. ii) If n >0 then n>0. iii) If n is an even number, then n² + 1 is prime. iv) If n is a positive integer, then nº >n! b) Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.) B(x): x is a ball R(x):...
Given Statement: Some popular bands are overrated. P = is popular Key of Predicate Symbols and Individual Constants: B = is a band 0 = is overrated Which expression is the best translation of the given statement above into predicate logic? (3x)(PxBx) (x)0x (3x)[(PxBx) • Ox] (3x)(PBX Ox) (x)[(Px > Bx) • Ox] Given Statement: Key of Predicate Symbols and Individual Constants: All citizens have a right to life, liberty, and the pursuit of happiness. C = is a citizen...
Do the following 3 things respectively with each of the two sentences given below 1. Translate it by using the defined predicate symbols and a quantifier 2. Transform it into an equivalent statement with a quantifier different from the one used in the lst translation (by applying QN); and 3. Articulate the corresponding sentence of the 2nd translation in ordinary English 5 15 Not all dogs bark. D: being a dog B: barking (SJ16] All philosophers are neither impractical nor...
please help
EXERCISES 4.2.5. Using the given symbolization key, translate each English-language asser tion into First-Order Logic u: The set of all animals. D: The set of all dogs. S: The set of all animals who like to swim f: Fergis b: Bertie e: Emerson r L y: s is larger than y. 1) Bertie is a dog who likes to swim 2) Bertie, Emerson, and Fergis are all dogs. 3) Emerson is larger than Bertie, and Fergis is larger...
I need help on the blue highlighted questions and 20 from the
last picture. Our professor doesn’t want a truth table. He wants a
proof.
In Exercises 13-24, use propositional logic to prove that the argument is valid. 13. (A VB')' A(BC) → (A' AC) 14. A' A( B A) →B' 15. (A →B) A [A → ( B C)] → ( AC ) 16.[( CD) →→[( CD) →D] 17. A' (A VB) →B Section 1.2 Propositional Logic 18. (A...
Using the book, write another paragraph or two: write 170
words:
Q: Compare the assumptions of physician-centered and
collaborative communication. How is the caregiver’s role different
in each model? How is the patient’s role different?
Answer: Physical-centered communication involves the specialists
taking control of the conversation. They decide on the topics of
discussion and when to end the process. The patient responds to the
issues raised by the caregiver and acts accordingly. On the other
hand, Collaborative communication involves a...
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