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) $E: a$ even number greater than $4$
(vi) $F: a$ number not less than $$$3$Also, find$A∪B, A∩B, B∪C, E∩F, D∩E, A-C, D-E, E∩F', F'$

Answer 1

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) $B = Φ$
(iii)$C =\\{3, 6\\}$
(iv) $D = \\{1, 2, 3\\}$
(v) $E = \\{6\\}$
(vi) $F = \\{3, 4, 5, 6\\}$
$A ∪ B = \\{1, 2, 3, 4, 5, 6\\}, A ∩ B = Φ$
$B ∪ C = \\{3, 6\\}, E ∩ F = \\{6\\}$
$D ∩ E =Φ,A - C = \\{1, 2, 4, 5\\}$
$F'=\\{1,2\\},E∩F'=Φ$

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