InterviewSolution
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InterviewSolution
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If `X={4^(n)-3n-1:n in N} and {9(n-1):n in N}`, the prove that `X sub Y`. |
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Answer» Let us find the elements of X Put `n=1,2,3,..." in "4^(n)-3n-1` `{:("At n=1",4^(n)-3n-1=4-3-1=0),("At n=2",4^(n)-3n-1=4^(2)-3(2)-1=9),("At n = 3",4^(n)-3n-4^(3)-3(3)-1=54),("At n = 4",4^(n)-3n-1=4^(4)-3(4)-1=243),(,......................................................),( :.,X={0,9,54,243,...}):}` Now, we will find the elements of Y `{:("At n=1",9(n-1)=9(1-1)=0),("At n=2",9(n-1)=9(2-1)=9),("At n=3",9(n-1)=9(3-1)=18),("At n=4",9(n-1)=9(4-1)=27),(,...........................................),( :.,{Y=0,9,18,27,...}):}` So, all elements of X are in Y and `X ne Y`. Therefore, `X sub Y`. |
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