Question

6. Let A = {
x|x € N and x + 1 < 8) and B = {xlx € N and x + 3 <= 5). Then, find AUB​

Answer 1

Correct Question:

If A={x:x, x€N,x+1<8} and B={x:x, x€N,x+3≤5}. Then,find (A U B)

Solution:

Given,

A={x:x, x€N,x+1<8} and B={x:x, x€N,x+3≤5}

★We need to express the following sets in roster from

Here,

•Consider x+1<8,

x+1<8

→x<8-1

→x<7

»Implies,values of x would be lesser than 7. i.e.,1,2,3,4,5 and 6

As x belongs to natural numbers we are not considering 0.

Thus, A={1,2,3,4,5,6}

•Consider x+3≤5

x+3≤5

→x+3<5 or x+3=5

→x<5-3 or x=5-3

→x<2 and x=2

→x≤2

»Implies,the values of x are 1 and 2

Thus,B={1,2}

To find: (A U B)

We need to find the union of the two given sets.

Note:

Union of two sets:

Union of two sets:All the elements of the two sets omitting from repeating the same elements

We have,

A={1,2,3,4,5,6} and B={1,2}

Now,

(A U B)

={12,3,4,5,6}