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Method and examples
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Select Operation
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Prove that any two expression is equal or not
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A =
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x `in` ,
x is
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- A = {x<=5; x in N}; B = {2<=x<=8; x in N}; C = {x<=3; x in N}
- A = {x^2<10; x in N}; B = {x<=1; x in N}; C = {1<=x<5; x in N}
- A = {1,2,3,4}; B = {3,4,5}; C = {1,3,5}
- A = {1,2,3,4}; B = {3,4,9,11}; C = {2,11,18,22}
- A = {2,3,6}; B = {3,5,6}; U = {1,2,3,4,5,6}
- A = {x<=9; x in N}; B = {3<=x<=7; x is odd}; C = {1<x<7; x is even}
- A = {1,2,3}; B = {2,3}
- A = {|x^3-2|<=25;x in N}; B = {1<x<5; x in N}; C = {x^4=81;x in N}
- A = {x^2-1 < 10;x in Z}; B = {|x-1|<2; x in N}; C = {|x|<=1;x in Z}
- A = {x^2<10; x in N}; B = {2,4,6}; C = {x^3-3x^2-4x=0}; U = {x<=10;x in N}
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Solution
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Solution provided by AtoZmath.com
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Prove that any two expression is equal or not calculator
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1. A = {x<=5; x in N}; B = {2<=x<=8; x in N}; C = {x<=3; x in N}
2. A = {x^2<10; x in N}; B = {x<=1; x in N}; C = {1<=x<5; x in N}
3. A = {1,2,3,4}; B = {3,4,5}; C = {1,3,5}
4. A = {2,3,6}; B = {3,5,6}; U = {1,2,3,4,5,6}
5. A = {x<=9; x in N}; B = {3<=x<=7; x is odd}; C = {1< x<7; x is even}
6. A = {|x^3-2|<=25;x in N}; B = {1< x<5; x in N}; C = {x^4=81;x in N}
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Example1. A = {1,2,3,4}, B = {3,4,5}, C = {1,3,5}, Prove that A intersect (B union C) = (A intersect B) union (A intersect C) ...
Solution:
Here `A={1,2,3,4}`,`B={3,4,5}`,`C={1,3,5}`
To find LHS = `A ∩ (B uu C)`
`B uu C = {3,4,5} uu {1,3,5}`
`= {color{red}{3},4,color{green}{5}} uu {1,color{red}{3},color{green}{5}}`
`= {3,4,5,1}`
`A nn (B uu C) = {1,2,3,4} nn {3,4,5,1}`
`= {color{red}{1},2,color{green}{3},color{blue}{4}} nn {color{green}{3},color{blue}{4},5,color{red}{1}}`
`= {1,3,4}`
`:. A ∩ (B uu C) = {1,3,4} ->(1)`
To find RHS = `(A ∩ B) uu (A ∩ C)`
`A nn B = {1,2,3,4} nn {3,4,5}`
`= {1,2,color{red}{3},color{green}{4}} nn {color{red}{3},color{green}{4},5}`
`= {3,4}`
`A nn C = {1,2,3,4} nn {1,3,5}`
`= {color{red}{1},2,color{green}{3},4} nn {color{red}{1},color{green}{3},5}`
`= {1,3}`
`(A ∩ B) uu (A ∩ C) = {3,4} uu {1,3}`
`= {color{red}{3},4} uu {1,color{red}{3}}`
`= {3,4,1}`
`:. (A ∩ B) uu (A ∩ C) = {3,4,1} ->(2)`
From (1) and (2)
`:. A ∩ (B uu C) = (A ∩ B) uu (A ∩ C)` (proved)
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