For any two sets A and B- prove by using of properties of sets that A - B-A-B-A- Also- verify this result by taking example-

We have LHS = (A ∪ B) A = (A ∪ B) ∩ A' = (A ∪ B) ∪ (B ∩ A) = ϕ∪ (B ∩ A') = B ∩ A' = B A = RHS Let A = { 1, 2, 4, 5,6}and B = {3,5,6,8} Now, LHS = ( A ...

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Standard IX

Mathematics

Distributive Property

For any two s...

Question

For any two sets A and B, prove by using of properties of sets that $(A \cup B) - A = B - A,$ Also,
verify this result by taking example.

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Solution

We have
$L H S = (A \cup B) - A = (A \cup B) \cap A^{'} = (A \cup B) \cup (B \cap A) = ϕ \cup (B \cap A^{'}) = B \cap A^{'} = B - A = R H S Let A = {1, 2, 4, 5, 6} and B = {3, 5, 6, 8} Now, LHS = (A \cup B) - A = {1, 2, 4, 5, 6} \cup {3, 5, 6, 8} - {1, 2, 4, 5, 6} = {1, 2, 3, 4, 5, 6, 8} - {1, 2, 4, 5, 6} = {3, 8} and RHS = B - A = {3, 5, 6, 8} - 1, 2, 4, 5, 6 = {3, 8} ∴ LHS = RHS$

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For any two sets A and B, prove by using of properties of sets that (A∪B)−A=B−A, Also, verify this result by taking example.

We have LHS=(A∪B)−A=(A∪B)∩A′=(A∪B)∪(B∩A)=ϕ∪(B∩A′)=B∩A′=B−A=RHSLet A ={1,2,4,5,6}andB={3,5,6,8}Now, LHS=(A∪B)−A={1,2,4,5,6}∪{3,5,6,8}−{1,2,4,5,6}={1,2,3,4,5,6,8}−{1,2,4,5,6}={3,8}and RHS=B−A={3,5,6,8}−1,2,4,5,6={3,8}∴LHS = RHS

For any two sets A and B, prove by using of properties of sets that $(A \cup B) - A = B - A,$ Also,
verify this result by taking example.