Recent content by YamiBustamante

Homework Statement [/B] Use the following values: E = 12.0 V , R1 = 35.0 Ω , R2 = 22.0 Ω , R3 = 41.0 Ω , and R4 = 14.0 Ω . Find the following currents: the current I1 through the resistor of resistance R1 = 35.0 Ω the current I2 through the resistor of resistance R2 = 22.0 Ω the current I3...

NEVERMIND I FIGURED IT OUT!

Homework Statement Suppose that A = { 1, 2, 3} , B = { 4, 5, 6} , R = { (1, 4), (1, 5), (2, 5), (3, 6)} , and S = { (4, 5), (4, 6), (5, 4), (6, 6)}. Note that R is a relation from A to B and S is a relation from B to B . Find the following relations: (a) S ◦ R . (b) S ◦ S−1...

So I have to prove "If (AxB)∩(BxA) ≠ ∅, then (A∩B) ≠ ∅." I wanted to prove by changing it's form. P = (AxB)∩(BxA) ≠ ∅ and Q = (A∩B) ≠ ∅ . The conditional statement is P implies Q and the new statement is not P or Q . P → Q = ¬ P∨Q They are equivalent. But how do I negate P? Would it be...

There's what I have so far. We assume that P(A) ⊆ P(B). This means that every element x that exists in P(A), also exits in P(B). By definition of a power set, x∈P(A) if x ⊆ A. Therefore, A∈P(A). Since P(A) ⊆ P(B), A∈P(B), meaning all x ⊆ A, x ∈ P(B). Furthermore, B∈P(B), meaning all x ⊆ B, x ∈...

Never mind. I figured it out. Thank you.

So the proof is false so therefore the theorem is false or is the theorem already false to begin with, so proof would also be false...

Incorrect Theorem: Suppose x and y are real numbers and x + y = 10, then x != 3 and y != 8. (a) What’s wrong with the following proof of the theorem? Proof. Suppose the conclusion of the theorem is false. Then x = 3 and y = 8. But then x + y = 11, which contradicts the given information...

So here is what I have: If x∉B then x∉C So, we can assume x∈A\B and since A\B and C are disjoined, then x∈A\B∩C which is true since x∉C. Would this be correct or is there any error in my logic?

Suppose that A\B is disjoint from C and x∈ A . Prove that if x ∈ C then x ∈ B . So I know that A\B∩C = ∅ which means A\B and C don't share any elements. But I don't necessarily understand how to prove this. I heard I could use a contrapositive to solve it, but how do I set it up. Which is P...

I don't understand how to get the charge density though and it's not even given to me in the problem, so how is that helpful?

Homework Statement Electric charge is uniformly distributed inside a nonconducting sphere of radius 0.30 m. The electric field at a point P, which is 0.50 m from the center of the sphere, is 15,000 N/C and is directed radially outward. At what distance from the center of the sphere does the...

Homework Statement [/B] An electron is launched at a 45∘ angle and a speed of 5.0×10^6 m/s from the positive plate of the parallel-plate capacitor shown in the figure (Figure 1) . The electron lands 4.0 cm away. a) What is the electric field strength inside the capacitor? b) What is the...

Homework Statement [/B] A 2.4 kg piece of wood slides on the surface shown in the figure . The curved sides are perfectly smooth, but the rough horizontal bottom is 31m long and has a kinetic friction coefficient of 0.27 with the wood. The piece of wood starts from rest 4.0m above the rough...

It's done :D