Answer:
A. X∪Y = {25, 36, 49}
B. X∩Y = ∅ i.e empty set
C. X' = {21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48}
D. X′∩Y∩Z = ∅
Step-by-step explanation:
We'll begin by determining the universal set (ε), set X, set Y and set Z.
This can be obtained as follow:
ε = {whole numbers less than 50 but greater than 20}
ε = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49}
X = {perfect squares}
X = {25, 36, 49}
Y = {factors of 12}
Y = ∅ i.e empty
Z = {prime numbers}
Z = {23, 29, 31, 37, 41, 43, 47}
A. Determination of X∪Y
X = {25, 36, 49}
Y = ∅
X∪Y =?
X∪Y => combination of elements in set X and Y without repeating any element in both X and Y.
X∪Y = {25, 36, 49}
B. Determination of X∩Y
X = {25, 36, 49}
Y = ∅
X∩Y =?
X∩Y => elements common to both set X and Y
X∩Y = ∅ i.e empty
C. Determination of X′
ε = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49}
X = {25, 36, 49}
X' =?
X' => elements in the universal set but not found in set X.
X' = {21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48}
D. Determination of X′∩Y∩Z
X' = {21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48}
Y = ∅
Z = {23, 29, 31, 37, 41, 43, 47}
X′∩Y∩Z =?
X′∩Y∩Z => elements common to set X', Y and Z
X′∩Y∩Z = ∅
