# Misc 13 - Chapter 1 Class 12 Relation and Functions (Term 1)

Last updated at Jan. 28, 2020 by Teachoo

Miscellaneous

Misc 1
Deleted for CBSE Board 2022 Exams

Misc 2 Deleted for CBSE Board 2022 Exams

Misc 3 Important Deleted for CBSE Board 2022 Exams

Misc. 4 Important

Misc 5

Misc 6 Deleted for CBSE Board 2022 Exams

Misc 7 Deleted for CBSE Board 2022 Exams

Misc. 8 Important

Misc 9 Important Deleted for CBSE Board 2022 Exams

Misc 10 Important

Misc 11 (i) Important Deleted for CBSE Board 2022 Exams

Misc 11 (ii) Deleted for CBSE Board 2022 Exams

Misc 12 Deleted for CBSE Board 2022 Exams

Misc 13 Important Deleted for CBSE Board 2022 Exams You are here

Misc 14 Important Deleted for CBSE Board 2022 Exams

Misc 15

Misc 16 (MCQ) Important

Misc 17 (MCQ) Important

Misc 18 Deleted for CBSE Board 2022 Exams

Misc 19 (MCQ) Important Deleted for CBSE Board 2022 Exams

Chapter 1 Class 12 Relation and Functions (Term 1)

Serial order wise

Last updated at Jan. 28, 2020 by Teachoo

Misc 13 Given a non-empty set X, let *: P(X) × P(X) → P(X) be defined as A * B = (A − B) ∪ (B − A), ∀ A, B ∈ P(X). Show that the empty set ϕ is the identity for the operation * and all the elements A of P(X) are invertible with A−1 = A. (Hint: (A − ϕ) ∪ (ϕ – A) = A and (A − A) ∪ (A − A) = A * A = ϕ). Identity e is the identity of * if a * e = e * a = a Here, A * ϕ = (A − ϕ) ∪ (ϕ – A) = A ∪ ϕ = A & ϕ * A = (ϕ − A) ∪ (A – ϕ) = ϕ ∪ A = A Since, A * ϕ = ϕ * A = A 𝛟 is the identity of operation * Invertible An element a in set is invertible if, there is an element in set such that , a * b = e = b * a Here, e = ϕ , b = A Now, A * A = (A − A) ∪ (A – A) = ϕ ∪ ϕ = ϕ & A * A = (A − A) ∪ (A – A) = ϕ ∪ ϕ = ϕ Since, A * A = ϕ = A * A Hence, all the elements A of P(X) are invertible with inverse of A = A