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 $\mathrm{A} \cup \mathrm{B}, \mathrm{A} \cap \mathrm{B}, \mathrm{B} \cup \mathrm{C}, \mathrm{E} \cap \mathrm{F}, \mathrm{D} \cap \mathrm{E}, \mathrm{A}-\mathrm{C}, \mathrm{D}-\mathrm{E}, \mathrm{E} \cap \mathrm{F}^{\prime}, \mathrm{F}^{\prime}$
When a die is thrown, the sample space is given by S = {1, 2, 3, 4, 5, 6}.
Accordingly:
(i) $A=\{1,2,3,4,5,6\}$
(ii) $B=\Phi$
(iii) $C=\{3,6\}$
(iv) $D=\{1,2,3\}$
(v) $E=\{6\}$
(vi) $F=\{3,4,5,6\}$
$A \cup B=\{1,2,3,4,5,6\}, A \cap B=\Phi$
$B \cup C=\{3,6\}, E \cap F=\{6\}$
$D \cap E=\Phi, A-C=\{1,2,4,5\}$
$\mathrm{D}-\mathrm{E}=\{1,2,3\}, \mathrm{F}^{\prime}=\{1,2\}, \mathrm{E} \cap \mathrm{F}^{\prime}=\phi$
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