Question

A die is thrown. Describe the following events:
$\left(i\right)A:$ a number less than $7$
$\left(ii\right)B:$ a number greater than $7$
$\left(iii\right)C:$ a multiple of $3$
$\left(iv\right)D:$ a number less than $4$
$\left(v\right)E:$ an even number greater than $4$
$\left(vi\right)F:$ a number not less than $3$
Also find $A\cup B,A\cap B,B\cup C,E\cap F,D\cap E,A-C,D-E,E\cap F^{\prime },F^{\prime }$

Answer 1

Given : A die is rolled
The possible outcomes
$S=\{1,2,3,4,5,6\}$.
$A:$ a number less than $7$
$A=\{1,2,3,4,5,6\}$
$B:$ a number greater than $7$
$B=\left\{\varphi \right\}$
$C:$ a multiple of $3$
$C=\{3,6\}$
$D:$ a number less than $4$
$D=\{1,2,3\}$
$E:$ an even number greater than $4$
$E=\left\{6\right\}$
$F:$ a number not less than $3$
$F=\{3,4,5,6\}$

Calculating
$A\cup B,A\cap B,B\cup C,E\cap F,D\cap E,A-C,D-E,E\cap F^{\prime },F^{\prime }$

$A\cup B=\{1,2,3,4,5,6\}\cup \varphi$
$=\{1,2,3,4,5,6\}$

$A\cap B=\{1,2,3,4,5,6\}\cap \varphi$
$=\varphi$

$B\cup C=\varphi \cup \{3,6\}$
$=\{3,6\}$

$E\cap F=\left\{6\right\}\cap \{3,4,5,6\}$
$=\left\{6\right\}$

$D\cap E=\{1,2,3\}\cap \left\{6\right\}$
$=\left\{\varphi \right\}$

$A-C=\{1,2,3,4,5,6\}-\{3,6\}$
$=\{1,2,4,5\}$

$D-E=\{1,2,3\}-\left\{6\right\}$
$=\{1,2,3\}$

$E\cap F^{\prime }=\left\{6\right\}\cap \{1,2\}$
$=\varphi$.

$F^{\prime }=S-F=\{1,2,3,4,5,6\}-\{3,4,5,6\}$
$=\{1,2\}$