Let Σ = {0, 1}, and let L10101 ⊆ Σ∗ be a language of exactly all the strings that contain the substring ‘10101’. Define the language J10101 = { ⟨M⟩ | M is a deterministic Turing machine, and L(M) = L10101 } . Show that J10101 is an undecidable language.

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XOR function or exclusive OR function was introduced in Excel 2013. This function is available under excel logical functions. For the given statement, the XOR function will return true only when either of the statements is true. It returns false when both the statements are true or when both the statements are false.