Question

If ln is the set of n number of natural numbers then prove that I6 union (I8-I5) =I8
​

Answer 1

SOLUTION

GIVEN

$\sf{I_n}$ is the set of n number of natural numbers

TO PROVE

$\sf{I_6 \cup \:(I_8 - I_5) = I_8}$

EVALUATION

Here it is given that $\sf{I_n}$ is the set of n number of natural numbers

Now

$\sf{I_5= \{1,2,3,4,5 \} }$

$\sf{I_6= \{1,2,3,4,5,6 \} }$

$\sf{I_8= \{1,2,3,4,5,6,7,8 \} }$

Now

$\sf{I_8 - I_5 }$

$\sf{= \{6,7,8 \} }$

Now

$\sf{I_6 \cup \:(I_8 - I_5) }$

$\sf{= \{1,2,3,4,5,6,7,8 \} \: \cup \: \{6,7,8 \} }$

$\sf{= \{1,2,3,4,5,6,7,8 \} \: }$

$\sf{ = I_8 }$

Hence proved

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