Math  /  Discrete

Question3) لأى ثلاث مجمو عات C, B , A أثبت صحة القو انين التالية : (i) AΔ(BΔC)=(AΔB)ΔCA \Delta(B \Delta C)=(A \Delta B) \Delta C (ii) A(BC)c=(AB)(AC)A \cap(B \cup C)^{c}=(A-B) \cup(A-C) (iii) (AB)(AcC)(BC)=(AB)(AcC)(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've proven all three (well, two and corrected one) set identities!
Specifically, we showed that AΔ(BΔC)=(AΔB)ΔCA \Delta (B \Delta C) = (A \Delta B) \Delta C, A(BC)c=(AB)(AC)A \cap (B \cup C)^c = (A - B) \cap (A - C), and (AB)(AcC)(BC)=(AB)(AcC)(A \cap B) \cup (A^c \cap C) \cup (B \cap C) = (A \cap B) \cup (A^c \cap C).

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord