Question

A die is thrown. Describe the following events.
(i) A: a number less than 7
(ii) B: a number greater than 7
(iii) C: a multiple of 3
(iv) D: a number less than 4
(v) E: an even number greater than 4
(vi) 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

When a die is thrown then $S=\{1,2,3,4,5,6\}$
(i) $7=\{1,2,3,4,5,6\}$
(ii) B: a number greater than 7$=\varphi$
(iii) C : a multiple of $3=\{3,6\}$
(iv) D: a number less than $4=\{1,2,3\}$
(v) E: an even number greater than $4=\left\{6\right\}$
(vi) F: a number not less than $3=\{3,4,5,6\}$
Now $A\cup B=\{1,2,3,4,5,6\}$
$A\cap B=\varphi$
$B\cup C=\{3,6\}$
$E\cap F=\left\{6\right\}$
$A-C=\{1,2,4,5\}$
$D-E=\{1,2,3\}$
$E\cap F^{\prime }=\varphi$
$F^{\prime }=\{1,2\}$