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The notation: ∃! x P(x)
means “There exists a unique x such that P(x)”.
If the domain consists of all integers, what are the truth values of these statement?
1. ∃! x(x > 1)
2. ∃! x(x
2 = 1)
3. ∃! x(x + 3 = 2x)
4. [∃! xP(x)] → [∃xP(x)]
5. [∀xP(x)] → [∃! xP(x)]
6. [∃! x~P(x)] → [~∀xP(x)]
7. ∃! x(x = x + 1)
8. ~(∃! xP(x)) → ∀xP(x)
9. (∃xP(x) ∧ ∃xQ(x)) → ∃x (P(x) ∧ Q(x))
10. (∀xP(x) ∨ ∀xQ(x)) → ∀x (P(x) ∧ Q(x))
Determine if the following argument is valid or if it exhibits the converse or the inverse error. Use symbols to write the logical form of argument. If the argument is valid, identify the rule of inference that guarantees its validity. Otherwise, state whether the converse or the inverse error is made.
If at least one of these two numbers is divisible by 6,
then the product of these two numbers is divisible by 6.
Neither of these two numbers is divisible by 6.
∴ The product of these two numbers is not divisible by 6.
1)Translate these statements into English, where C(x) is “x is a comedian” and F(x) is “x is funny” and the domain consists of all people.
a) ∀x(C(x) → F(x))
b) ∀x(C(x) ∧ F(x))
c) ∃x(C(x) → F(x))
2) Somie, a leader of the underworld, was killed by one of his own band of four henchmen. Detective Sharp interviewed the men and determined that all were lying except for one. He deduced who killed Somie on the basis of the following statements:
a. Socko: Lefty killed Somie.
b. Fats: Muscles didn’t kill Somie.
c. Lefty: Muscles was shooting craps with Socko when Somie was knocked off.
d. Muscles: Lefty didn’t kill Somie.
Who did kill Somie?
show that p ↔ q and (p^q) v (¬p^¬q) are logical equivalent
I would like to ask for help with discrete mathematics, especially two's complement
- Using two’s complement representation throughout your calculation, find 31 – 19.
- Using Euclidean algorithm, find the GCD of 123 and 411.
solve the recurrence relation using generating functions An+1-An=3n )n>0 with AQ=1
Translate the statement into propositional logic using the propositions provided.
You cannot edit a protected Wikipedia entry unless you are an administrator. Express your answer in terms of e: “You can edit a protected Wikipedia entry” and a: “You are an administrator.”
Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives.
a) No one is perfect.
b) Not everyone is perfect.
c) All your friends are perfect.
d) At least one of your friends is perfect.
e) Everyone is your friend and is perfect.
f) Not everybody is your friend or someone is not perfect.
Show that (p ∧ q) → (p ∨ q) is a tautology.
Which of these are propositions? What are the truth values of those that are propositions? Write P and its truth value either True or False if Proposition and NP if not a proposition and write what made it not a proposition.
a) Do not pass go.
b) What time is it?
c) 4 + x = 5.
d) The moon is made of green cheese.
e) 2n≥ 100.
f) 1+2=5
#339914 on Dec 2023