In general, what do you need to show to prove the following?:
(For example: to prove something is a group you'd show closure,
associative, identity, and invertibility)
a. Ring
b. Subring
c. Automorphism of rings
d. Ring homomorphism
e. Integral domain
f. Ideal
g. Irreducible
h. isomorphic
Prove that every sequence in a discrete metric space converges
and is a Cauchy sequence.
This is all that was given to me... so I am unsure how I am
supposed to prove it....
How do you determine the
properties of steam or refrigerant 134a from the properties if you
know only specific internal energy and specific volume (or specific
enthalpy and specific entropy) at the thermodynamic
state?
NOTE- If it is true, you need to prove it and If it is false,
give a counterexample
f : [a, b] → R is continuous and in the open interval (a,b)
differentiable.
a) If f(a) ≥ f(b), then exists a ξ ∈ (a,b) with f′(ξ) ≤ 0.(TRUE
or FALSE?)
b) If f is reversable, then f −1 differentiable. (TRUE or
FALSE?)
c) If f ′ is limited, then f is lipschitz. (TRUE or FALSE?)
NOTE- If it is true, you need to prove it and If it is false,
give a counterexample
f : [a, b] → R is continuous and in the open interval (a,b)
differentiable.
a) If f(a) ≥ f(b), then exists a ξ ∈ (a,b) with f′(ξ) ≤ 0. (TRUE
or FALSE?)
b) If f is reversable, then f −1 differentiable. (TRUE or
FALSE?)
c) f is constant ⇐⇒ ∀x∈(a,b): f′(x)=0 (TRUE or FALSE?)
2. Prove the following properties.(b) Prove that x + ¯ xy = x + y.3. Consider the following Boolean function: F = x¯ y + xy¯ z +
xyz(a) Draw a circuit diagram to obtain the output F. (b) Use the
Boolean algebra theorems to simplify the output function F into the
minimum number of input literals.
3) Now you will plan for your retirement. To do this we need to
first determine a couple of values.
a. How much will you invest each year? Even $25 a month is a
start ($300 a year), you’ll be surprised at how much it will earn.
You can choose a number you think you can afford on your life
circumstances or you can dream big. State what you will use for P,
r, and n to earn credit. (3...