Mathematics, 14.09.2019 02:30, iBrain
Question 3. let f: x --> y be a function. (a) recall that for c cy, the inverse image of c is the set f-1(c) = {x e x|f(x) e c}. let a, b cy. prove that f-1(anb) cf-1(a) n f-1(b). (b) recall that for d c x, the image of d under f is the set f(d) = {f(x) e yx e x}. let a, b c x. prove that f(an b) c f(a)n f(b). find an example of a function f and sets a and b such that f(anb) = ø but f(a) n f(b) + ø.
Answers: 3
. Then, we can do that proving that every element of 
is an element of 
too.
. From the definition of inverse image we know that 
, which is equivalent to 
and 
. But, as 
we can affirm that 
and, because 
.
.
. Here we will follow the same strategy of the above exercise.
. Then, there exists 
such that 
. But, as 
and 
. From this, we deduce 
and 
. Therefore, 
.
for every real number 
. Take the sets 
and 
.
=Ø, so 
=Ø. But 
and 
, so 
.
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Question 3. let f: x --> y be a function. (a) recall that for c cy, the inverse image of c is th...
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