Answer:
8 elements
Step-by-step explanation:
From the question given above, the following data were obtained:
Universal set (S) = 132
Set A = 63
Set B = 35
n(AuB)ᶜ = 89
n(A but not in B) =?
Next, we shall determine the number of elements common to both set A and Set B. This can be obtained as follow:
Let the number common to both set A and B be x i.e
(AnB) = x
nA = 63
nB = 35
n(AuB)ᶜ = 89
Universal set (S) = 132
S = nA + nB + n(AuB)ᶜ – (AnB)
132 = 63 + 35 + 89 – x
132 = 187 – x
Collect like terms
132 – 187 = – x
– 55 = – x
Divide both side by –1
x = –55 /–1
x = 55
Thus, the number of elements common to set A and B is 55.
Finally, we shall determine the number of elements in A but not in B as follow:
nA = 63
n(AnB) = 55
n(A but not in B) =?
n(A but not in B) = nA – n(AnB)
n(A but not in B) = 63 – 55
n(A but not in B) = 8
Thus, 8 elements are in set A but not in set B.
