दो पासे फेंके जाते हैं । घटनाएँ A, B और C निम्नलिखित प्रकार से हैं :
A : पहले पासे पर सम संख्या प्राप्त होना ।
B : पहले पासे पर विषम संख्या प्राप्त होना ।
C : पासों पर प्राप्त संख्याओं का योग `le` 5 होना ।
निम्नलिखित घटनाओं का वर्णन कीजिए
(i) A'
(ii) B - नहीं
(iii) A या B
(iv) A और B
(v) A किंतु C नहीं
(vi) B या C
(vii) B और C
(viii) `A nn B' nn C'`

Explanation

दो पाँसों को फेकने पर ,
प्रतिदर्श समष्टि
S = `{:{("(1,1)" , "(1,2)" , "(1,3)", "(1,4)","(1,5)" ,"(1,6)"),("(2,1)","(2,2)","(2,3)","(2,4)","(2,5)","(2,6)"),("(3,1)","(3,2)","(3,3)","(3,4)","(3,5)","(3,6)"),("(4,1)","(4,2)","(4,3)","(4,4)","(4,5)","(4,6)"),("(5,1)","(5,2)","(5,3)","(5,4)","(5,5)","(5,6)"),("(6,1)","(6,2)","(6,3)","(6,4)","(6,5)","(6,6)"):}}`
अब A = पहले पासे पर सम संख्या प्राप्त होने की घटना
`{:{("(2,1)","(2,2)","(2,3)","(2,4)","(2,5)","(2,6)"), ("(4,1)","(4,2)","(4,3)","(4,4)","(4,5)","(4,6)"),("(6,1)","(6,2)","(6,3)","(6,4)","(6,5)","(6,6)"):}}`
B = पहले पासें पर विषम संख्या प्राप्त होने की घटना
`{:{("(1,1)" , "(1,2)" , "(1,3)", "(1,4)","(1,5)" ,"(1,6)"), ("(3,1)","(3,2)","(3,3)","(3,4)","(3,5)","(3,6)"), ("(5,1)","(5,2)","(5,3)","(5,4)","(5,5)","(5,6)"):}}`
C = पासों पर प्राप्त संख्याओं का योग `le` 5 प्राप्त होने की घटना
{ (1,1) ,(1,2) , (2,1) , (1,3) ,(2,2), (3 , 1), (1, 4) ,(2, 3) , (3, 2) , ( 4, 1) }
(i) A' = S - A
= `{:{("(1,1)" , "(1,2)" , "(1,3)", "(1,4)","(1,5)" ,"(1,6)"), ("(3,1)","(3,2)","(3,3)","(3,4)","(3,5)","(3,6)"), ("(5,1)","(5,2)","(5,3)","(5,4)","(5,5)","(5,6)"):}}` उत्तर
(ii) B - नहीं = S - B
`{:{("(2,1)","(2,2)","(2,3)","(2,4)","(2,5)","(2,6)"), ("(4,1)","(4,2)","(4,3)","(4,4)","(4,5)","(4,6)"),("(6,1)","(6,2)","(6,3)","(6,4)","(6,5)","(6,6)"):}}` उत्तर
(iii) A या B
= `{:{("(1,1)" , "(1,2)" , "(1,3)", "(1,4)","(1,5)" ,"(1,6)"),("(2,1)","(2,2)","(2,3)","(2,4)","(2,5)","(2,6)"),("(3,1)","(3,2)","(3,3)","(3,4)","(3,5)","(3,6)"),("(4,1)","(4,2)","(4,3)","(4,4)","(4,5)","(4,6)"),("(5,1)","(5,2)","(5,3)","(5,4)","(5,5)","(5,6)"),("(6,1)","(6,2)","(6,3)","(6,4)","(6,5)","(6,6)"):}}` उत्तर
(iv) A और B = `phi`
(v) A किंतु C नहीं = A - C
{(2,4) , (2,5) , (2,6) , (4,2) ,(4,3) , (4,4) , (4,5) , (4, 6) , (6 , 1) , (6, 2) , (6,3) , ( 6 , 4) , (6 , 5) , (6, 6) }
(vi) B या C = `B uu C`
`{{:("(1,1)" , "(1,2)" , "(1,3)", "(1,4)","(1,5)" ,"(1,6)"),("(2,1)","(2,2)","(2,3)" , , ,),("(3,1)","(3,2)","(3,3)","(3,4)","(3,5)","(3,6)"),("(4,1)" , , , , ,),("(5,1)","(5,2)","(5,3)","(5,4)","(5,5)","(5,6)"):}}` उत्तर
(vii) B और C = ` B nn C`
= { ( 1,1) , (1,2) , (1,3) , (1,4) , (3,1) , (3,2) } उत्तर
(Viii) C' = S - C
`{:(, , , ,"(1,5)" ,"(1,6)"),(, , ,"(2,4)","(2,5)","(2,6)"),(, , "(3,3)", "(3,4)","(3,5)","(3,6)"),(,"(4,2)","(4,3)","(4,4)","(4,5)","(4,6)"),("(5,1)","(5,2)","(5,3)","(5,4)","(5,5)","(5,6)"),("(6,1)","(6,2)","(6,3)","(6,4)","(6,5)","(6,6)"):}}`
अब `A nn B' nn C'`
= ` A nn C' becasue B' = A ( "भाग II स" )`
= `{:{(, , ,"(2,4)","(2,5)","(2,6)"), (, "(4,2)","(4,3)","(4,4)","(4,5)","(4,6)"),("(6,1)","(6,2)","(6,3)","(6,4)","(6,5)","(6,6)"):}}` उत्तर