Question

Find the union of the given pairs of set: A = {x : x is a natural number and 1 < x ≤ 6 }, B = {x x is a natural number and 6 < x < 10 }

Answer 1

concept : if two sets A and B are given, then union of set A and B is written as $A\cup B$. This is the set of all distinct elements that are in Both A or B. see figure, Venn diagram shown, represents that the $\cup$ of any two sets will give all the members of the two sets together, and not replicating the common member twice.

now , given set A = {x :x is a natural number and 1 < x ≤ 6 } e.g., A = {2, 3, 4, 5, 6}

set B = {x : x is a natural number and 6 < x < 10}
e.g., B = {7, 8, 9}

All the members of both sets together are ; 2, 3, 4, 5, 6, 7, 8, 9.

from rule of union, we don't have to replicate members. So, the members of union of these two sets are 2, 3, 4, 5, 6, 7, 8, 9.
therefore , $A\cup B$ = {2, 3, 4, 5, 6, 7, 8, 9}

Answer 2

Answer:

A U B = { 2,3,4,5,6,7,8,9 }

Step-by-step explanation:

A={x:x is a natural number

and 1 < x ≤ 6 }

=> A = { 2,3,4,5,6 }

B = { x:x is a natural number

and 6<x<10 }

=> B = { 7, 8 , 9 }

A U B = { 2,3,4,5,6}U{7,8,9}

= { 2,3,4,5,6,7,8,9 }

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