Chapter 2: Q45E (page 137)
Show that if \(A\)is an infinite set, then whenever \(B\)is a set, \(A \cup B\)is also an infinite set.
\(A \cup B\) is a finite set, as \(A\)is an infinite set and we have \(A \subseteq (A \cup B)\)
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Question: Let\(f(x) = ax + b\) and \(g(x) = cx + d\) where a, b, c, and d are constants. Determine necessary and sufficient conditions on the constants a, b, c, and d so that \(f \circ g = g \circ f\)
what is the empty set? Show that the empty set is a subset of every set.
Question: Consider these functions from the set of students in a discrete mathematics class. Under what conditions is the function one-to-one if it assigns to a teacher his or her
Office
Assigned bus to chaperone in a group of buses taking students on a field trip
Salary
Social security number
Let and let for all . Show that f(x) is strictly decreasing if and only if the functionrole="math" localid="1668414965156" is strictly increasing.
Suppose that g is a function from A to B and f is a function from B to C.
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