# Set theory Questions and answers

Topics
41). If $$\Large n \left(A\right)=6, n \left(B\right)=5, n \left(A\cap B\right)=3$$ then find $$\Large n \left(A\cup B\right)$$
 A). 11 B). 9 C). 8 D). None of these
42). lf $$\Large A=\{ 1, 2, 3, 4, 5, 6 \},\ B=\{ 4, 5, 6 \}$$, then $$\Large n \left(A\cap B\right)$$
 A). 3 B). 6 C). 4 D). 2
43). If $$\Large n \left(p \left(A\right)=16 \right)$$ then what is the value of $$\Large n \left(A\right)$$
 A). 12 B). 4 C). 8 D). 2
44). If $$\Large A=\{ 4, 5, 6, 7, 8, 9, 10 \},\ A\cap B=\{ 6, 7, 8 \},\ A\cup B=\{ 4, 5, 6, 7, 8, 9, 10, 11, 12 \}$$, then find B.
 A). $$\Large \{ 4, 5, 6, 7, 8 \}$$ B). $$\Large \{ 6, 7, 8, 11, 12 \}$$ C). $$\Large \{ 4, 5, 7, 10, 11, 12 \}$$ D). None of these
45). If $$\Large E=\{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \},\ A=\{1, 2, 3, 4, 5 \},\ B=\{2, 4, 6, \}$$ then find $$\Large \left(A\cup B\right)'$$
 A). $$\Large \{ 8, 9 10 \}$$ B). $$\Large \{ 7, 8, 9 10 \}$$ C). $$\Large \{ 6, 7, 8, 9, 10 \}$$ D). cannot be found

46). $$\Large n \left(A\cup B\right)=8,\ n \left(A\right)=6,\ n \left(B\right)=4$$ find $$\Large n \left(A\cap B\right)$$
 A). 10 B). 7 C). 2 D). 4
47). In an examination $$\Large 77 ^{\circ}$$ pupils passed in English $$\Large 65 ^{\circ}$$ students passed in Mathematics and $$\Large 50 ^{\circ}$$ students passed both in English and Mathematics. Then how many percentage of students fail in both the subjects.
 A). 16 B). 8 C). 12 D). 20
48). In a school 420 students appeared for Mathematics and English examination. Out of this 285 students passed in Mathematics, 290 students passed in English and 260 students passed in both the subjects, then how many students fail in both the subjects.
 A). 105 B). 12 C). 135 D). 180
49). In an examination, $$\Large 45 ^{\circ}$$ students failed in Science and $$\Large 56 ^{\circ}$$ failed in Mathematics if $$\Large 16 ^{\circ}$$ failed in both Science and Mathematics the percentage of those who passed in both the subject is.
 A). 15 B). 31 C). 49 D). 42
50). In a class 42 students passed in Physics, 50 students passed in Chemistry and 50 students passed in Mathematics 26 students were passed in Physics and Chemistry, 24 students passed in Chemistry and Mathematics and 23 students were passed in Physics and Mathematics. If 11 students were passed in all the subjects, find the number of students appeared for the examination.
 A). 80 B). 60 C). 70 D). 90
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