Question

If A, B, C are three sets such that AAB = AAC then

(A) A = B

(B) A = B = C

(C) B = C​

Answer 1

${\huge{\overbrace{\underbrace{\orange{ANSWER!!}}}}}$

Lencho wrote the letter to God as he thought that he would be the only one to help him in his bad times. He wrote a letter addressing to God to send him 100 pesos so that he and his family can survive in such a difficult situation. The postmaster received the letter written by Lencho.

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Answer 2

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$\sf\red{⟶}$Let x∈C

Suppose x∈A⇒x∈A∩C

⇒x∈A∩B(∵A∩C=A∩B)

Thus x∈B

Again suppose x∈/A⇒x∈C∪A

⇒x∈B∪A⇒x∈B

Hence C⊆B .......(1)

Similarly we can show that B⊆C .....(2)

Commbining (1) and (2) we get B=C

$\underline{\red{\sf{\blue\:Thank \ чou ♡ }}}$