Question

Find the union of the given pairs of set: A = {x : x is a natural number and multiple of 3}, B = {x : x is a natural number less than 6}

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.

given, set A = {x : x is a natural number and multiple of 3}.e.g., A = {3, 6, 9, 12, 15, 18, .....}
B = {x : x is a natural number less than 6}e.g., B = {1, 2, 3, 4, 5}
All the members of both sets together are 3, 6, 9, 12, 15, 18, ..........., 1, 2, 3, 4, 5

from rule of union, we don't have to replicate members. So, the members of union of these two sets are 1, 2, 3, 4, 5, 6, 9, 12, 15, 18, ..........

hence, $A\cup B$ = {1, 2, 3, 4, 5, 6, 9, 12, .... }

Answer 2

Answer:

AUB = {1,2,3,4,5,6,9,12,15,18,...}

Step-by-step explanation:

A = {x:x is a natural number and

multiple of 3 }

=> A = { 3,6,9,12,15,18,21,24,...}

B = { x : x is a natural number

less than 6 }

B = { 1,2,3,4,5 }

AUB = { 3,6,9,12,15,18,....}U

{ 1,2,3,4,5}

= {1,2,3,4,5,6,9,12,15,18,21,24,...}

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