Consider the following two sets A & B: A= {4, 8, 12, 16, … } B = {1, 3, 5, 7, 9, … } Let be a function from z × z to , such that f(m,n) = (m*m)-(n*n). . i) Show that every element of the set A has a preimage under the function f. Type/Insert your answer here! ii) Show that every element of the set B has a preimage under the function f. Type/Insert your answer here!
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Given:
Consider the following two sets A & B:
A= {4, 8, 12, 16, … }
B ={1, 3, 5, 7, 9, … }
Let f be a function from z × z to , such that .
1) Show that every element of the set A has a preimage under the function f.
Solution:
2)Show that every element of the set B has a preimage under the function f.
Solution:
Answer:\\
(1) for
(2) for