## Transcribed Text

2
Propositional equivalences
Usc logical to that (p
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7
Set identities
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10
Image, Pre-image
Suppose f : R R where f(x) -
1. If S = {o|12. If T = ((3.4,5), ind f -(1) .
12
Euclidean algorithm
Use the Bucideon find ged(123,277)
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You may submit an answer In inspera, or a handwritten solution
al sleps of your calculal om caplicity, adting noe ness as required of you in use
the For Instonce
1-2-111
2=1-2+0
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15
Mathematical induction
mathematical induction to prowe that 52,38 2) = for all Integens n. 1
=
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FIII in your answer here
17
Structural induction
Let S be the subset of the ordered pa s of integers derined recursively by
Bess step (0.0) E S
Recursivo If (a,6) : S. then (a c 1) c Send ia 1.6 1) C S.
a) List the elements of 8 produced by the frst three applications of the recursive definition
b) Use structural induction to a < bahenever (a.ò) € S
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