CS-170J - Modelling Computing Systems - IT Assignment Help

Assignment Task

Question 1
Specify the domain, codomain, and range of the following functions:
(a) The function that assigns to each real number its square.
(b) The function that assigns to each real number its cube.
(c) The function that assigns to each nonnegative integer the largest power of 10 smaller than it.
(d) The function that assigns to two real numbers their midpoint.

Question 2
Find f, g and g, f, where f and g are following functions from R to R:
f(x) = x
2 − 1 and g(x) = x
2 + 1.

Question 3
Real time strategy games usually have two aspects: economy and army. A player who is good/bad at developing their economy is said to have good/bad macro. A player who is good/bad at controlling their army is said to have good/bad micro.
The abilities to macro and micro are independent of each other, i.e. a player can be good at both, bad at both, or good at one and bad at the other. Consider the following relations on the set of players:
BetterMacro = {(x, y) : x has better macro than y}
WorseMacro = {(x, y) : x has worse macro than y}
BetterMicro = {(x, y) : x has better micro than y}
WorseMicro = {(x, y) : x has worse micro than y}
StrictlyBetter = {(x, y) : x has better macro and better micro than y}
StrictlyWorse = {(x, y) : x has worse macro and worse micro than y}
Even = {(x, y) : (x has better macro and worse micro than y) or (x has worse macro and better micro than y)}
(a) Define BetterMacro in terms of WorseMacro.
(b) Define BetterMicro in terms of Even and WorseMacro.
(c) Define Even in terms of StrictlyBetter.

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