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secondary 4 | E Maths
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I am stuck with this question. Would appreciate help from anyone. Thanks in advance.
If all students of the school play at least one of the four games, then none of the students are left alone without a sport.
(B u F u H u V)' = ∅ (no one is outside of any of the sports)
(b)
No student plays both basketball and hockey.
B n H = ∅ (no common player in basketball and hockey)
(c)
Some students play both football and volleyball.
F n V ≠ ∅ (here we cannot definitively say how many, so the only way we can say is "not zero")
All those who play volleyball also play basketball.
This means that the basketball group must have wholly contained the volleyball group (it's like saying, Tampines is part of Singapore)
B u V = V
Note that the reverse is not necessarily true (eg Singapore is not just "part of Tampines")
(e)
Those who do not play basketball play football.
Note, again, that the reverse is not necessarily true, so those who play football may or may not play basketball
B' u F = F
(f)
Those who play hockey do not play volleyball.
Note, again, that the reverse is not necessarily true, so those who do not play volleyball may or may not play hockey.
H u V' = V'
(g)
Gary plays basketball, football and hockey
Gary must be a "member" of the three sports. We use "an element of" symbol.
Gary ∈ (B n F n H)
Hilda plays volleyball but not football.
This time, there is only one person, so of course the reverse has to be true.
Hilda ∈ (V n F')
(i)
Ian plays basketball and football but not volleyball.
The notation is similar to the previous one.
Ian ∈ (B n F n V')
(j)
Julia plays hockey only.
This means that Julia does not play the other sports.
Julia ∈ (H n B' n F' n V')
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