6. (6 points) Let our universe be the set of all people, P(x) denote x is...

Transcribed Image Text:

6. (6 points) Let our universe be the set of all people, P(x) denote "x is a professor", and C(x) denote "x is a clown". Translate the following logical statements into English. (a) Vx(P(x) → C(x)) (b) Vx(P(x) ▼ C(x)) (c) x (P(x) ^ C(x)) 7. (5 points) By using logical equivalences, prove that ¬q V (p → q) is a tautology. (Write the names of the rules that you apply.) 8. (6 points) By using logical equivalences, prove the following equivalency. (Write the names of the rules that you apply.) (pg) V (p^¬q) = ¬q 9. (4 points) Let the universe be the set of all integers. Express the following statement in pred- icate logic: "the product of every two negative integers is positive". Identify the predicate(s) and the final statement. 6. (6 points) Let our universe be the set of all people, P(x) denote "x is a professor", and C(x) denote "x is a clown". Translate the following logical statements into English. (a) Vx(P(x) → C(x)) (b) Vx(P(x) ▼ C(x)) (c) x (P(x) ^ C(x)) 7. (5 points) By using logical equivalences, prove that ¬q V (p → q) is a tautology. (Write the names of the rules that you apply.) 8. (6 points) By using logical equivalences, prove the following equivalency. (Write the names of the rules that you apply.) (pg) V (p^¬q) = ¬q 9. (4 points) Let the universe be the set of all integers. Express the following statement in pred- icate logic: "the product of every two negative integers is positive". Identify the predicate(s) and the final statement.

Answer rating: 100% (QA)

Lets address each point one by one 6 Translation of logical statements into English a xPx Cx This translates to For every person x if x is a professor ... View the full answer