If S and T are non-empty sets. Prove that there exists a one-one correspondence(bijective) between 𝑆 × 𝑇 and 𝑇 × 𝑆

Question

If S and T are non-empty sets. Prove that there exists a one-one correspondence(bijective) between 𝑆 × 𝑇 and 𝑇 × 𝑆
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Solution 1

To prove that there exists a one-one correspondence (bijective function) between S x T and T x S, we need to construct a function that maps each element in S x T to a unique element in T x S, and vice versa.

Let's define a function f: S x T -> T x S as follows:

For any element (s, t) in S x T, le Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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