Question

if a^b=b^a then prove (a/b)^(a/b)=a^{(a/b)-2}​

Answer 1

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Class 11

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>>If A and B are sets, then p...

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If A and B are sets, then prove that A - B, A∩B and B - A are pair wise disjoint.

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Solution

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Given:-A&B are two sets.

Pair wise disjoint means no two elements of any two sets are equal.

So,we have to proof:

(A−B)∩(B−A)=(A−B)∩(A∩B)=

(B−A)∩(A∩B)=ϕ

Letxϵ(A−B)∩(B−A)

∴xϵ(A−B)&xϵ(B−A)

xϵA−(i)orx∈

/

B−(ii)

xϵB−(iii)orx∈

/

A−(iv)

from(i)&(iv) we are at contradiction

Hence (A−B)∩(B−A)=ϕ

Now,let ∴xϵ(A−B)∩(A∩B)

xϵAorx∈

/

B

xϵAorxϵB

So,xϵAorxϵBorx∈

/

B

So,xϵBorx∈

/

B are at conradiction.

(A−B)∩(A∩B)=ϕ