5. Rewrite the following proposition as unambiguous English sentences. The relevant predicates are defined as follows: Again, let’s let P be a set of all people a. A(x) means “x is teaching the AI course" b. T(x) means “x is taking AI course" c. F(x) means “x has a twitter account." d. C(x) means “x likes to read." For example, the proposition 3x { P[A(x)^ C(x)]} could be translated as "There is a person who is teaching and likes to read" P [T(x) → (F(x) C(x))] ?

5. Rewrite the following proposition as unambiguous English sentences. The relevant predicates are defined as follows: Again, let’s let P be a set of all people a. A(x) means “x is teaching the AI course" b. T(x) means “x is taking AI course" c. F(x) means “x has a twitter account." d. C(x) means “x likes to read." For example, the proposition 3x { P[A(x)^ C(x)]} could be translated as "There is a person who is teaching and likes to read" P [T(x) → (F(x) C(x))] ?

Name: 5. Rewrite the following proposition as unambiguousEnglish sentences.
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Description: 5. Rewrite the following proposition as unambiguousEnglish sentences. The relevant predicates are definedas follows: Again, let’s let P be a set of all peoplea. A(x) means “x is teaching the AI course"b. T(x) means “x is taking AI course"c. F(x) mea

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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13: Answer
please answer Q5 only, thanks.
7. Describe the following combined propositions as English sentences if s = heavy snow, C = flight canceled, and d=there are delays a. s→C b. sAc (s V c) • (d V c) e. sA (d V c) С. d d. s- 8. Convert the following expressions into DNF format (where ! is NOT) a. (x+y!z)(!x+y+!z) b. (ху)!(х+y) 9. Are the following expressions satisfiable? a. (x+y)(!x+!z)(!y+z)(x+!z+!y) b. (x+y)(!x+!z)(!y+z)(x+!z+!y)(!x+y+!z) 10. Draw circuit for the following expression !xy(!x+y)(x+y+!z)
Kindly answer both the questions asap
can you please explain why d is wrong and b is correct?
21. Let the following predicates be given. The domain is all computer science classes. I(r) = "x is interesting." U(x) = "x is useful." H(x, y) = “x is harder than y." M(x, y) = “x has more students than y." (a) Write the following statements in predicate logic. i. All interesting CS classes are useful. ii. There are some useful CS classes that are not interesting. iii. Every interesting CS class has more students than any non- interesting CS class. (b) Write the following predicate logic statement in everyday English. Don't just give a word-for-word translation; your sentence should make sense. (3)[I(x) A (Vy)(H(x,y)→ M(y, x))] (c) Formally negate the statement from part (b). Simplify your negation so that no quantifier lies within the scope of a negation. State which derivation rules you are using. (d) Give a translation of your negated statement in everyday English.
3. How to express the associativity of V as a tautology?
Using relational predicates ( e.g. F(s,m) for, say, s can fool m), translate the following sentences into predicate logic. You can use English words for the quantification symbols (such as For All x instead of v x) if necessary Also give the negatives of each sentence in English. a) Everybody can fool somebody b) There is no-one who can fool everyone. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).
A student club holds a meeting. The predicate M(x) denotes whether person x came to the meeting on time. The predicate O(x) refers to whether person x is an officer of the club. The predicate D(x) indicates whether person x has paid his or her club dues. The domain is the set of all members of the club. The names of the members and their truth values for each of the predicates is given in the following table. Indicate whether each expression is true or false. If a universal statement is not true, give a counterexample. If an existential statement is true, give an example. Name M(x) O(x) D(X) Hillary T F Bernie F F Donald F F Jeb F Carly F F Ex (M(x) A D(x)
3. Let us consider the propositional language where: A = "Peter does his homework" B = "Burt does his homework" C = "Andy does his homework" D = "Dexter comes to the party" Write the statement for the following symbols. (d) C → (~D → ~A) (e) (~D → C) A (D → ~B) (f) A A~BAC → ~D) a ( A a B → (D → C)