MAT 230 Discrete Mathematics| SNHU | Module 5 Problem Set 5–3 with Solutions (Grade A)

MODULE FIVE PROBLEM SET


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1

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PROBLEM 1
Indicate whether the two functions are equal. If the two functions are not equal,
then give an element of the domain on which the two functions have different values.

(a)
f : Z → Z, where f (x) = x2.
g : Z → Z, where g(x) = |x|2.


If we square an integer, an non negative result is obtained.
Considering
x2 = |x|2 for allx ∈ Z
Hence both functions are equal.


(b)
f : Z × Z → Z, where f (x, y) = |x + y|.
g : Z × Z → Z, where g(x, y) = |x| + |y|.


Let us say x and y have the same sign
f (x, y) = |x + y| = |x| + |y| = g(x, y)
But if x and y have opposite signs
f (x, y) /= g(x, y)
If x = -1, y = 1
Then
f (−1, 1) = | − 1 + 1| = |0| = 0
And
g(−1, 1) = | − 1| + |1| = 1 + 1 = 2
Therefore, the two functions are not equal.