The number that take (a) both PE is 6 girls (b) Gymnastic but not acrobat is 7 girls (c) At least one PE is 18 girls
How to determine the numbers?
Recall that Set theory is a branch of mathematical logic that studies sets, which can be informally described as collections of objects.
From the given parameters,
(a) The number that play both PE is given as
13 - x + x + 17 - x + 1 = 25
Solving the equation to get the value of x
13+17-x = 25
⇒ 31 -x =25
Collecting like terms we have
-x = 25 - 31
- x = -6
Dividing by a minus we have
x = 6
This means that 5 girls play both PE
(b) Number that play gymnastic but not acrobat is given as
Gymnastic only that is
13 - x
13 - 6 = 7 girls
(c) Number that play at least one game is calculated thus:
n(G) ∪ n(A)
That is (13 - x ) + (17 - x)
= 13-6 + 17 -6
7 + 11 = 18 girls