Question

If A={x|x belongs to R , x>=2} and B={x|x belongs to R, x<4} then the symmetric difference between A and B is?​

Answer 1

Question:

If A = { x : x € N and x < 20 } and

B = { x : x € N and x ≤ 5 } .

Write the set (A - B) in the set builder form.

Answer:

A - B = { x : x € N and 6 ≤ x ≤ 19 }

OR

A - B = { x : x € N and 5 < x < 20 }

Note:

• Set :-

A set is a well defined collection of distinct objects.

• Methods of representing a set :-

i. Roster or tabular or listed form

ii. Set-builder form

• Roster form :-

✓ All the elements are listed.

✓ Elements are separated by commas .

✓ Elements are enclosed within braces { } .

✓ The order of writing elements doesn't matter.

✓ The elements are not repeated.

• Set-builder form :-

✓ The common properties of elements are written.

✓ The elements are described using symbols like x,y,z (mostly described by x).

✓ Whole description of elements are enclosed within braces { } .

• Difference of sets :-

✓ The difference of two sets A and B in the order (also called "relative complement of B in A") is the set of all those elements of set A which are not the elements of set B.

✓ It is denoted by (A - B).

Solution:

We have two sets A and B in their set-builder form as;

A = { x : x € N and x < 20 }

B = { x : x € N and x ≤ 5 }

Here,

The roster form of the given sets A and B will be given as;

A = { 1,2,3,...,19 }

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

Now,

The difference of sets A and B in order will be given as ;

=> A - B = { 1,2,3,..,19 } - { 1,2,3,4,5 }

=> A - B = { 6,7,8,...19 }

Hence,

The difference set (A - B) in roster form is ;

A - B = { 6,7,8,...19 }.

Now,

The difference set (A - B) in set-builder form will be given as ;

A - B = { x : x € N and 6 ≤ x ≤ 19 }

OR

A - B = { x : x € N and 5 < x < 20 }

Hence,

Required difference set in set-builder form is;

A - B = { x : x € N and 6 ≤ x ≤ 19 }

OR

A - B = { x : x € N and 5 < x < 20 }