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1.Write the Molecular Formula of 2-methyl-1-butene.
2. Write the equation if the compound in number 1 will be subjected to hydrobromination.
3. The product in number 2 is treated with Grignard Reagent. Write the two steps chemical reactions.
4. Write the molecular formula of the major product in number 3
5. The answer in number 4 is exposed to combustion. Write and balance the chemical reaction.
Translate each of these nested quantifications into an English statement that expresses a mathematical fact. The domain in each case consists of all real numbers.
a) ∃x ∀y(x + y = y)
b) ∀x ∀y (((x ≥ 0) ∧ (y < 0)) → (x − y > 0))
c) ∃x ∃y(((x ≤ 0) ∧ (y ≤ 0)) ∧ (x − y > 0))
d) ∀x ∀y((x ≠ 0) ∧ (y ≠ 0) ↔ (xy ≠ 0))
A water sample was reported to contain 250 ppm CaCO3. How many grams of CaCO3 is present in 4 liters of water.
Apply definition of antiderivative and find area under the curve of f(x) = x^1/2 between x=0 and
x=1
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))
Find absolute maximum and minimum of the function f(x) = 2x^2- 5 in [-1, 2].
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?
6. Determine whether each of the following statements about Fibonacci numbers is true or false. Note
The first 10 terms of the Fibonacci sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34, and 55.
a. If n is even, then F is an odd number.
b. 2F-Fn-2 = Fn+1 for n 23
Many countries abroad do not teach CAT as a school subject, but only concentrate on computer literacy at school level.
Construct and motivate your own point of view on the necessity for CAT as a school subject.
