Explain the relationship between equivalence relations on a set and partitions of this set.

Can someone explain equivalence classes in discrete math?

The magnetic dipole moment of the iron atom is about $2.1 \times 10 ^ { - 23 } \mathrm { A } \cdot \mathrm { m } ^ { 2 }$. (a) Calculate the maximum magnetic dipole moment of a domain consisting of $10 ^ { 19 }$ iron atoms. (b) What current would have to flow through a single circular loop of wire of diameter 1.0 cm to produce this magnetic dipole moment?

Identify the following term or individuals and explain their significance. nonaggression pact

Solve the equation. |2x + 3.6| = 9.8

Is this true? If false, explain briefly. AP-value below 0.05 is always considered sufficient evidence to reject a null hypothesis.

Explain the relationship between equivalence relations on a set and partitions of this set.

a) Define (using truth tables) the disjunction, conjunction, exclusive or, conditional, and biconditional of the propositions p and q. b) What are the disjunction, conjunction, exclusive or, conditional, and biconditional of the propositions “I’ll go to the movies tonight” and “I’ll finish my discrete mathematics homework”?

Some of the movies with all-time-high box office grosses include Avatar ($761 million), The Avengers ($618 million), Titanic ($601 million), The Dark Knight ($533 million), Star Wars ($461 million), Shrek 2 ($437 million), and E.T. the Extra Terrestrial ($435 million). Suppose that you have all seven films on DVD and decide, over the course of a week, to view some, all, or none of these films. How many viewing options do you have?

Suppose tan x = k where k is a constant and $\pi<x<\frac{3 \pi}{2}$. Write expressions for sin x and cos x in terms of k.

Under the notation of the preceding exercise prove that if $H\trianglelefteq S_\Omega$ and $H\neq 1$ then $A\leq H$, i.e., $A$ is the unique (nontrivial) minimal normal subgroup of $S_\Omega$.

In which of the following equations does sulfuric acid act as an oxidizing agent? In which does it act as an acid? Explain.

$$4 \mathrm { H } ^ { + } ( a q ) + \mathrm { SO } _ { 4 } ^ { 2 - } ( a q ) + 2 \mathrm { Nal } ( s ) \longrightarrow 2 \mathrm { Na } ^ { + } ( a q ) + \mathrm { I } _ { 2 } ( s ) + \mathrm { SO } _ { 2 } ( g ) + 2 \mathrm { H } _ { 2 } \mathrm { O } ( l )$$

Give an order-of-magnitude estimate for the mass of: a. an apple b. this physics book c. a soccer ball.

Calculate $\Delta H ^ { \circ }$ for each of the following reactions, which occur in the atmosphere.

$$2 \mathrm { NO } ( g ) + \mathrm { O } _ { 2 } ( g ) \rightarrow 2 \mathrm { NO } _ { 2 } ( g )$$