Question

2) Take the set of natural numbers from 1 to 20 as universal set and show set X

and Y using Venn diagram.

(i) X = { x  |  x Î N, and 7 < x < 15}

(ii) Y = { y  |  y Î N, y is prime number from 1 to 20}​

Answer 1

Step-by-step explanation:

Given :-

Take the set of natural numbers from 1 to 20 as universal set.

To find :-

Show set X and Y using Venn diagram.

(i) X = { x  |  x Î N, and 7 < x < 15}

(ii) Y = { y  |  y Î N, y is prime number from 1 to 20}

Solution :-

Given that :

The set of natural numbers from 1 to 20

U = { 1,2,3,4,...,20 }

Where U is the universal set.

X = { x  |  x Î N, and 7 < x < 15}

=> X = { 8,9,10,11,12,13,14}

and

Y = { y  |  y Î N, y is prime number from 1 to 20}

=> Y = { 2,3,5,7,11,13,17,19}

Venn diagrams are drawn see the above attachment

Used formulae:-

• The set containing all the elements in the other sets observing the given sets is called the universal set. It is denoted by U .

• Sets are represented by some closed figures like triangles, Rectangles ,Squares and ovals.

• Generally Universal set is represented by Rectangles.

• The sets are generally represented by triangles.

• This representation was introduced by John Vennman and Euler.

• So these diagrams are called Venn-Euler diagrams or Venn diagrams.

• Set theory was introduced by George Cantor.