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

Given that:

Universal set, U = {1, 2, 3, 4, ......, 17, 18, 19, 20}

Set $X = \{ x | x \in N, and\ 7 < x < 15\}$

i.e. X contains the natural numbers between 7 and 15. (7 and 15 excluded from the set.)

Another set

$Y = \{y| y \in N, \text{y is prime number from 1 to 20}\}$

Numbers which are prime and are between 1 to 20 are the elements of set Y.

Now, let us write the elements of set X and Y:

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

Number of elements in X, n(X) = 7

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

Number of elements in Y, n(Y) = 8

Common elements in "X and Y":

Set $X \cap Y$ = {11, 13}

Number of elements in the Common elements set, n($X \cap Y$) = 2

Elements in the union of two sets i.e. set X or Y:

$X \cup Y$= {2, 3, 5, 7, 8, 9, 10, 11, 12 ,13, 14, 17, 19}

n($X \cup Y$) = 13

Please refer to the attached diagram for the Venn Diagram representation.

Description of Venn Diagram:

Universal set U is represented by a rectangle.

The two sets X and Y are represented as circles inside the rectangle showing Universal set U.

As we can clearly see, there are 2 elements common in sets X and Y so, the two circles representing X and Y so the two circles are overlapping.

Universal set has a few elements which are not in sets X and Y that is why there is white space shown in Universal set rectangle.