# A die is thrown. Describe the following events:

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

Solution:

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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