Math Problem Statement

Jika A = {a, b, {a, c}, Ø} dan B = {a, {a}, d, e}, tentukan himpunan berikut: (a) A - Ø (b) A - {Ø} (c) {{a, c}} - A (d) A ⊕ B (e) {a} - {A} (f) P(A-B) (g) Ø - A (h) B² (i) A ∪ (B ∩ A) (j) A ∩ P(A)

Solution

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Math Problem Analysis

Mathematical Concepts

Set Theory
Set Difference
Symmetric Difference
Power Set
Intersection
Union

Formulas

A - B = {x | x ∈ A and x ∉ B}
A ⊕ B = (A - B) ∪ (B - A)
Power Set P(A) = the set of all subsets of A
Intersection A ∩ B = {x | x ∈ A and x ∈ B}
Union A ∪ B = {x | x ∈ A or x ∈ B}

Theorems

Properties of Set Operations
Subset and Power Set Theorem

Suitable Grade Level

University Level or Advanced High School

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