1. Examples
1. A = {1,2,3,4}, B = {3,4,5}, Find A - B ...
Solution:
Here `A={1,2,3,4},B={3,4,5}`
`A - B = {1,2,3,4} - {3,4,5}`
`= {1,2,color{red}{3},color{green}{4}} - {color{red}{3},color{green}{4},5}`
`= {1,2}`
2. A = {1,2,3,4}, B = {3,4,5}, Find B-A ...
Solution:
Here `A={1,2,3,4},B={3,4,5}`
`B - A = {3,4,5} - {1,2,3,4}`
`= {color{red}{3},color{green}{4},5} - {1,2,color{red}{3},color{green}{4}}`
`= {5}`
3. A = {x<=5; x in N}, B = {2<=x<=8; x in N}, C = {x<=3; x in N}, Prove that A - (B intersect C) = (A - B) union (A - C) ...
Solution:
`A={x<=5; x in N}`
`:.A={1,2,3,4,5}`
`B={2<=x<=8; x in N}`
`:.B={2,3,4,5,6,7,8}`
`C={x<=3; x in N}`
`:.C={1,2,3}`
To find LHS = `A - (B ∩ C)`
`B nn C = {2,3,4,5,6,7,8} nn {1,2,3}`
`= {color{red}{2},color{green}{3},4,5,6,7,8} nn {1,color{red}{2},color{green}{3}}`
`= {2,3}`
`A - (B ∩ C) = {1,2,3,4,5} - {2,3}`
`= {1,color{red}{2},color{green}{3},4,5} - {color{red}{2},color{green}{3}}`
`= {1,4,5}`
`:. A - (B ∩ C) = {1,4,5} ->(1)`
To find RHS = `(A - B) uu (A - C)`
`A - B = {1,2,3,4,5} - {2,3,4,5,6,7,8}`
`= {1,color{red}{2},color{green}{3},color{blue}{4},color{maroon}{5}} - {color{red}{2},color{green}{3},color{blue}{4},color{maroon}{5},6,7,8}`
`= {1}`
`A - C = {1,2,3,4,5} - {1,2,3}`
`= {color{red}{1},color{green}{2},color{blue}{3},4,5} - {color{red}{1},color{green}{2},color{blue}{3}}`
`= {4,5}`
`(A - B) uu (A - C) = {1} uu {4,5}`
`= {1} uu {4,5}`
`= {1,4,5}`
`:. (A - B) uu (A - C) = {1,4,5} ->(2)`
From (1) and (2)
`:. A - (B ∩ C) = (A - B) uu (A - C)` (proved)
This material is intended as a summary. Use your textbook for detail explanation.
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