Problem 5
Civen \(A=\\{4,5,6\\}, B=\\{3,4,6,7\\},\) and \(C=\\{2,3,6\\},\) verify the distributive law.
Problem 6
Verify the distributive law by means of Venn diagrams, with different orders of successive shading.
Problem 6
Find: \((a) x^{3} / x^{-3}\) \((b)\left(x^{1 / 2} \times x^{1 / 3}\right) / x^{2 / 3}\)
Problem 6
For the function \(y=-x^{2}\), if the domain is the set of all nonnegative real numbers, what will its range be?
Problem 7
In the theory of the firm, economists consider the total cost \(C\) to be a function of the output level \(Q: C=f(Q)\) (a) According to the definition of a function, should each cost figure be associated with a unique level of output? (b) Should each level of output determine a unique cost figure?
Problem 7
Enumerate all the subsets of the set \(\\{5,6,7\\}\)
Problem 8
If an output level \(Q_{1}\) can be produced at a cost of \(C_{1}\), then it must also be possible (by being less efficient) to produce \(Q_{1}\) at a cost of \(C_{1}+\$ 1,\) or \(C_{1}+\$ 2,\) and so on. Thus it would seem that output \(Q\) does not uniquely determine total cost \(C\). If \(s 0\), to write \(C=f(Q)\) would violate the definition of a function. How, in spite of the this reasoning, would you justify the use of the function \(C=f(Q) ?\)
Problem 8
Enumerate all the subsets of the set \(S=\\{a, b, c, d\\} .\) How many subsets are there altogether?
Problem 9
Example 6 shows that \(\varnothing\) is the complement of \(U\). But since the null set is a subset of any set, \(\varnothing\) must be a subset of \(U\). Inasmuch as the term "complement of \(U^{\prime \prime}\) implies the notion of being not in \(U\), whereas the term "subset of \(U^{\prime \prime}\) implies the notion of being in \(U,\) it seems paradoxical for \(\varnothing\) to be both of these. How do you resolve this paradox?
