Why do the ferromagnetic elements come from the middle of the group of transition elements or from the middle of the rare earth elements rather than the ends of the respective groups?

Find sets (when possible) satisfying each of the following conditions.

c. Number of elements in $E$ plus number of elements in $F$ equals number of elements in $E \cup F$.

If $A=\left(a_{i j}\right)$ is a square matrix, then the elements $a_{i i}$ are called the diagonal elements. How do the diagonal elements of A and $^{t} A$ differ?

The community theater is selling tickets for their fall play. On the first day of ticket sales, the theater sold 9 adult tickets and 3 student tickets for a total of $75. The theater collected$67 on the second day by selling 5 adult tickets and 8 student tickets. What are the prices of one adult ticket and one student ticket?

For each of the following elements, use the table on the inside front cover of the book to give the chemical symbol and atomic number and to specify whether the element is a metal or a nonmetal. Also give the named family to which the element belongs (if any).

d. beryllium

If three circuit elements are connected in parallel, which of the following statements is true?

(a) The voltage across the circuit elements is always the same.

(b) The current through the circuit elements is always the same.

(c) The power is always the same in all three circuit elements.

Choose the appropriate description for the term the difference of $B$ and $A$. Assume that $A$ and $B$ are sets. A. the set of elements in $A$ that are not in $B$ B. the set of elements common to both $A$ and $B$ C. the set of elements in the universal set that are not in $A$ D. the set of elements in $B$ that are not in $A$ E. the set of ordered pairs such that each first element is from $A$ and each second element is from $B$, with every element of $A$ paired with every element of $B$ F. the set of elements that are in $A$ or in $B$ or in both $A$ and $B$

The atomic number of beryllium is one less than that of boron, which follows it on the periodic table. Strontium, which is directly below beryllium in period 5 of the periodic table has 34 more protons and 34 more electrons than beryllium. However, the properties of beryllium resemble the much larger strontium more than those of similar-sized boron. The properties of beryllium are more similar to those of strontium than those of boron because. A. A strontium atom is larger than a boron atom. B. Strontium and beryllium are both reactive nonmetals. C. A strontium atom has more electrons than a boron atom. D. Strontium has the same number of valence electrons as beryllium.

$$\text { Show that } A _ { 5 } \text { has } 24 \text { elements of order } 5,20 \text { elements of order } 3 , \text { and }15 \text { elements of order } 2$$

Choose the appropriate description for the term the difference of $A$ and $B$. Assume that $A$ and $B$ are sets. A. the set of elements in $A$ that are not in $B$ B. the set of elements common to both $A$ and $B$ C. the set of elements in the universal set that are not in $A$ D. the set of elements in $B$ that are not in $A$ E. the set of ordered pairs such that each first element is from $A$ and each second element is from $B$, with every element of $A$ paired with every element of $B$ F. the set of elements that are in $A$ or in $B$ or in both $A$ and $B$

Choose the appropriate description for the term the complement of $A$. Assume that $A$ and $B$ are sets. A. the set of elements in $A$ that are not in $B$ B. the set of elements common to both $A$ and $B$ C. the set of elements in the universal set that are not in $A$ D. the set of elements in $B$ that are not in $A$ E. the set of ordered pairs such that each first element is from $A$ and each second element is from $B$, with every element of $A$ paired with every element of $B$ F. the set of elements that are in $A$ or in $B$ or in both $A$ and $B$

Draw a Hasse diagram for a partially ordered set that has two maximal elements and two minimal elements and is such that each element is comparable to exactly two other elements.

Let P be a subposet of Q. This means that the elements of P are a subset of the elements of Q, and the relation between elements of P are exactly the same as their relation in Q (i.e., x$\leq$y in P iff x$\leq$y in Q). Prove that dim P $\leq$ dim Q.

Most of the elements are solids at $30^{\circ} \mathrm{C}$. Give three examples of elements that are liquids and three examples of elements that are gases at $30^{\circ} \mathrm{C}$.