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Math  /  Discrete

Question(3) لأى ثلاث مجموعات C, B , A أثبت صحة القو انين التالية : (i) AΔ(BΔC)=(AΔB)ΔCA \Delta(B \Delta C)=(A \Delta B) \Delta C (ii) A∩(B∪C)c=(A−B)∪(A−C)A \cap(B \cup C)^{c}=(A-B) \cup(A-C) (iii) (A∩B)∪(Ac∩C)∪(B∩C)=(A∩B)∪(Ac∩C)(A \cap B) \cup\left(A^{c} \cap C\right) \cup(B \cap C)=(A \cap B) \cup\left(A^{c} \cap C\right)

Studdy Solution
We have **proven** all three set equalities:
1. \(A \Delta (B \Delta C) = (A \Delta B) \Delta C\)
2. \(A \cap (B \cup C)^c = (A - B) \cup (A - C)\)
3. \((A \cap B) \cup (A^c \cap C) \cup (B \cap C) = (A \cap B) \cup (A^c \cap C)\)

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