function, range and symmetric difference
$f(A)triangle f(B) subseteq f(Atriangle B)$. Is it true for all functions $f: (Acup B) rightarrow Y$? I think it is true but I can't prove it. Can you give me a hint, please? If there is $f(x)in f(A)$, $f(x)notin f(B)$ and $f(x)in f(Acap B) Rightarrow f(x)in f(B)$ because $f(Acap B) in f(B)$, so, $f(x) in f(B)$. Contradiction. Is this a right solution?
functions
add a comment |
$f(A)triangle f(B) subseteq f(Atriangle B)$. Is it true for all functions $f: (Acup B) rightarrow Y$? I think it is true but I can't prove it. Can you give me a hint, please? If there is $f(x)in f(A)$, $f(x)notin f(B)$ and $f(x)in f(Acap B) Rightarrow f(x)in f(B)$ because $f(Acap B) in f(B)$, so, $f(x) in f(B)$. Contradiction. Is this a right solution?
functions
Do you mean $f(A) = {f(a)mid ain A}$
– amWhy
Nov 25 at 19:11
What is the definition of $f(A Delta B)$? What happens when you take an element $y in f(A) Delta f(B)$, is it contained in $f(ADelta B)$?
– Bman72
Nov 25 at 19:11
Use the definition of symmetric difference: ${f(a)mid ain A} triangle {f(b)mid bin B)$. Compare with ${f(x) mid (xin A land xnotin B) lor (x notin A land xin B)}$
– amWhy
Nov 25 at 19:16
add a comment |
$f(A)triangle f(B) subseteq f(Atriangle B)$. Is it true for all functions $f: (Acup B) rightarrow Y$? I think it is true but I can't prove it. Can you give me a hint, please? If there is $f(x)in f(A)$, $f(x)notin f(B)$ and $f(x)in f(Acap B) Rightarrow f(x)in f(B)$ because $f(Acap B) in f(B)$, so, $f(x) in f(B)$. Contradiction. Is this a right solution?
functions
$f(A)triangle f(B) subseteq f(Atriangle B)$. Is it true for all functions $f: (Acup B) rightarrow Y$? I think it is true but I can't prove it. Can you give me a hint, please? If there is $f(x)in f(A)$, $f(x)notin f(B)$ and $f(x)in f(Acap B) Rightarrow f(x)in f(B)$ because $f(Acap B) in f(B)$, so, $f(x) in f(B)$. Contradiction. Is this a right solution?
functions
functions
edited Nov 25 at 19:21
asked Nov 25 at 19:02
user596269
Do you mean $f(A) = {f(a)mid ain A}$
– amWhy
Nov 25 at 19:11
What is the definition of $f(A Delta B)$? What happens when you take an element $y in f(A) Delta f(B)$, is it contained in $f(ADelta B)$?
– Bman72
Nov 25 at 19:11
Use the definition of symmetric difference: ${f(a)mid ain A} triangle {f(b)mid bin B)$. Compare with ${f(x) mid (xin A land xnotin B) lor (x notin A land xin B)}$
– amWhy
Nov 25 at 19:16
add a comment |
Do you mean $f(A) = {f(a)mid ain A}$
– amWhy
Nov 25 at 19:11
What is the definition of $f(A Delta B)$? What happens when you take an element $y in f(A) Delta f(B)$, is it contained in $f(ADelta B)$?
– Bman72
Nov 25 at 19:11
Use the definition of symmetric difference: ${f(a)mid ain A} triangle {f(b)mid bin B)$. Compare with ${f(x) mid (xin A land xnotin B) lor (x notin A land xin B)}$
– amWhy
Nov 25 at 19:16
Do you mean $f(A) = {f(a)mid ain A}$
– amWhy
Nov 25 at 19:11
Do you mean $f(A) = {f(a)mid ain A}$
– amWhy
Nov 25 at 19:11
What is the definition of $f(A Delta B)$? What happens when you take an element $y in f(A) Delta f(B)$, is it contained in $f(ADelta B)$?
– Bman72
Nov 25 at 19:11
What is the definition of $f(A Delta B)$? What happens when you take an element $y in f(A) Delta f(B)$, is it contained in $f(ADelta B)$?
– Bman72
Nov 25 at 19:11
Use the definition of symmetric difference: ${f(a)mid ain A} triangle {f(b)mid bin B)$. Compare with ${f(x) mid (xin A land xnotin B) lor (x notin A land xin B)}$
– amWhy
Nov 25 at 19:16
Use the definition of symmetric difference: ${f(a)mid ain A} triangle {f(b)mid bin B)$. Compare with ${f(x) mid (xin A land xnotin B) lor (x notin A land xin B)}$
– amWhy
Nov 25 at 19:16
add a comment |
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Do you mean $f(A) = {f(a)mid ain A}$
– amWhy
Nov 25 at 19:11
What is the definition of $f(A Delta B)$? What happens when you take an element $y in f(A) Delta f(B)$, is it contained in $f(ADelta B)$?
– Bman72
Nov 25 at 19:11
Use the definition of symmetric difference: ${f(a)mid ain A} triangle {f(b)mid bin B)$. Compare with ${f(x) mid (xin A land xnotin B) lor (x notin A land xin B)}$
– amWhy
Nov 25 at 19:16