Question

for any sets A,B,C, prove that A∩(B⊕C)=(A∩B)⊕(B∩C)

for any sets A,B,C, prove that A∩(B⊕C)=(A∩B)⊕(B∩C)

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Means

So that or (by definition of symmetric difference)

So that or

Which means or

Combining these, we get (the left side is not B but A in the last set as can be checked on some online reference such as wikipedia, image below for reference:)

Thus, we have

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove that for all sets A, B, C, A ∩ (B ∩ C) = (A ∩...
Prove that for all sets A, B, C, A ∩ (B ∩ C) = (A ∩ B) ∩ C Prove that for all sets A, B, A \ (A \ B) = A ∩ B.
Let A, B, C be sets. Prove that (A \ B) \ C = (A \...
Let A, B, C be sets. Prove that (A \ B) \ C = (A \ C) \ (B \ C).
Prove that for all sets A, B, and C, A × (B ∩ C) = (A...
Prove that for all sets A, B, and C, A × (B ∩ C) = (A × B) ∩ (A × C). Using set identity laws
Let A,B and C be sets, show(Prove) that (A-B)-C = (A-C)-(B-C).
Let A,B and C be sets, show(Prove) that (A-B)-C = (A-C)-(B-C).
Let A, B, C and D be sets. Prove that A \ B and C \...
Let A, B, C and D be sets. Prove that A \ B and C \ D are disjoint if and only if A ∩ C ⊆ B ∪ D.
(a) Give an argument (not using Venn diagrams) to prove that for any three sets A,...
(a) Give an argument (not using Venn diagrams) to prove that for any three sets A, B, and C, we have (A∪B)−C ⊆(A−(B∪C))∪(B−(A∩C)). (b) Does the equality (A∪B)−C=(A−(B∪C))∪(B−(A∩C)) hold for all sets A, B, and C? If so, prove it; if not, give three sets for which the equality fails.
Let A, B, C and D be sets. Prove that A\B ⊆ C \D if and...
Let A, B, C and D be sets. Prove that A\B ⊆ C \D if and only if A ⊆ B ∪C and A∩D ⊆ B
Let A and B be sets. Prove that A ⊆ B if and only if A...
Let A and B be sets. Prove that A ⊆ B if and only if A − B = ∅.
If A and B are two finite sets. Prove that |A ∪ B| = |A| +...
If A and B are two finite sets. Prove that |A ∪ B| = |A| + |B| − |A ∩ B| is true.
Let A and B be sets. Prove that (A∪B)\(A∩B) = (A\B)∪(B\A)
Let A and B be sets. Prove that (A∪B)\(A∩B) = (A\B)∪(B\A)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT