Venn Diagrams and Operations on Sets

$A=\left\{a|a \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 10 \mathrm{between} 0 \mathrm{to} 100\right\}$

$B=\left\{b|b \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 15 \mathrm{between} 0 \mathrm{to} 100\right\}$

$C=\left\{c|c \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 30 \mathrm{between} 0 \mathrm{to} 100\right\}$

Find $A\cap B\cap C$.

$E=\left\{\mathrm{x}|\mathrm{x} \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 16 \mathrm{between} 0 \mathrm{to} 100\right\}$

$F=\left\{\mathrm{y}|\mathrm{y} \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 20 \mathrm{between} 0 \mathrm{to} 100\right\}$

$G=\left\{\mathrm{z}|\mathrm{z} \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 40 \mathrm{between} 0 \mathrm{to} 100\right\}$

Find $E\cap F\cap G$.

$A=\left\{\mathrm{x}|\mathrm{x} \mathrm{is} \mathrm{an} \mathrm{odd} \mathrm{number} \mathrm{between} 0 \mathrm{to} 20\right\}$

$B=\left\{\mathrm{y}|\mathrm{y} \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 3 \mathrm{between} 0 \mathrm{to} 20\right\}$

$C=\left\{\mathrm{z}|\mathrm{z} \mathrm{is} \mathrm{a} \mathrm{natural} \mathrm{number} \mathrm{between} 0 \mathrm{to} 20\right\}$

 $A\cap B\cap C=\left\{3,9,12,15\right\}$.

$A=\left\{\mathrm{x}|\mathrm{x} \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 5 \mathrm{between} 0 \mathrm{to} 50\right\}$

$B=\left\{\mathrm{y}|\mathrm{y} \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 10 \mathrm{between} 0 \mathrm{to} 50\right\}$

$C=\left\{\mathrm{z}|\mathrm{z} \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 20 \mathrm{between} 0 \mathrm{to} 50\right\}$

$\therefore$ $A\cap B\cap C$$=B$.

$A=\left\{\mathrm{x}|\mathrm{x} \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 4 \mathrm{between} 0 \mathrm{to} 30\right\}$

$B=\left\{\mathrm{y}|\mathrm{y} \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 8 \mathrm{between} 0 \mathrm{to} 30\right\}$

$C=\left\{\mathrm{z}|\mathrm{z} \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 12 \mathrm{between} 0 \mathrm{to} 40\right\}$

Find $A\cap B\cap C$.

$X=\left\{x|x \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 3 \mathrm{in} \mathrm{between} 0 \mathrm{to} 30\right\}$

$Y=\left\{\mathrm{y}|\mathrm{y} \mathrm{is} \mathrm{a} \mathrm{odd} \mathrm{number} \mathrm{between} 11 \mathrm{and} 30\right\}$

$X\cap Y=\left\{21,27\right\}$

$P=\left\{x|\mathrm{x} \mathrm{is} \mathrm{multiple} \mathrm{of} 5 \mathrm{between} 0 \mathrm{and} 100\right\}$

$Q=\left\{\mathrm{y}|\mathrm{y} \mathrm{is} \mathrm{multiple} \mathrm{of} 10 \mathrm{within} 100\right\}$

The set $R=Q$ where $R=P\cap Q$

From the adjoining Venn diagram, find the following sets :

$(\mathrm{A}\cup \mathrm{B}\cup \mathrm{C})\text{'}$

From the Venn diagram, find

(A $\cup$ B $\cup$ C)

$C=\left\{x|\mathrm{x} \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 3 \mathrm{within} 20\right\}$

$D=\left\{\mathrm{y}|\mathrm{y} \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 9 \mathrm{within} 30\right\}$

Find the set $X$ where $X=C\cap D$

From the Venn diagram, find the following sets :

A $\cup$ B $\cup$ C

$A=\left\{x|\mathrm{x} \mathrm{is} \mathrm{a} \mathrm{prime} \mathrm{number} \mathrm{within} 20\right\}$

$B=\left\{\mathrm{y}|\mathrm{y} \mathrm{is} \mathrm{odd} \mathrm{numbers} \mathrm{between} 0 \mathrm{to} 20\right\}$

Find the set $C$ where $C=A\cap B$

Using information given in the Venn diagram, find the following.

$n(A\cup B)$

Using information given in the Venn diagram, find the following.

$(A\cup B\cup C)$

$A=\left\{a,b\right\}$, $B=\left\{e,f\right\}$. Verify closure property of union of two sets.

$A=\left\{a,b,c\right\}$, $B=\left\{d,e,f\right\}$. Verify closure property of union of two sets.

$A=\left\{1,2,3\right\}$, $B=\left\{2,3,4,5\right\}$. Verify closure property of union of two sets.

$A=\left\{1,2,3,4\right\}$, $B=\left\{2,3,4,5,6\right\}$. Verify closure property of union of two sets.

$A=\left\{1,2\right\}$, $B=\left\{2,3\right\}$. Verify closure property of union of two sets.

$A=\left\{2,3,5\right\}$. Prove idempotent property of union of sets for given set.