Question

2. If n(A) =45, n(A ∪ B)=70, and n(A∩ B)=25, then find n(B)?​

Answer 1

Answer:

There is a mathematical relation between union and intersection of Two sets,

Let A and B be two sets, Then the formula will be,

n(AUB) = n(A)+ n(B) - n(AnB),

Given data, n(A) = 45,

n(B) = 52,

n(AUB) = 70,

n(AnB) = ?,

Substituting them in above Formula,

=> 70 = 45 + 52 - n(AnB),

=> 70 = 97 - n(AnB),

=> n(AnB) = 97-70,

=> n(AnB) = 27,

Therefore: The a answer is 27,

Answer 2

Answer:

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n(AuB) = n(A) + n (B) -n(AnB) —————-1

n(AuB) = n(A) + n (B) -n(AnB) —————-1We have n(AnB) = 25 and n(A-B) = 18

n(AuB) = n(A) + n (B) -n(AnB) —————-1We have n(AnB) = 25 and n(A-B) = 18With these 2 we can calculate n(A)

• n(AuB) = n(A) + n (B) -n(AnB) —————-1We have n(AnB) = 25 and n(A-B) = 18With these 2 we can calculate n(A)n(A-B) = n(A) - n(AnB)
• n(AuB) = n(A) + n (B) -n(AnB) —————-1We have n(AnB) = 25 and n(A-B) = 18With these 2 we can calculate n(A)n(A-B) = n(A) - n(AnB)18 = n(A) - 25

• n(AuB) = n(A) + n (B) -n(AnB) —————-1We have n(AnB) = 25 and n(A-B) = 18With these 2 we can calculate n(A)n(A-B) = n(A) - n(AnB)18 = n(A) - 25=> n(A) = 18 + 25 = 43

n(AuB) = n(A) + n (B) -n(AnB) —————-1We have n(AnB) = 25 and n(A-B) = 18With these 2 we can calculate n(A)n(A-B) = n(A) - n(AnB)18 = n(A) - 25=> n(A) = 18 + 25 = 43now to calculate n(B) we can substitute all the values in equation 1

• n(AuB) = n(A) + n (B) -n(AnB) —————-1We have n(AnB) = 25 and n(A-B) = 18With these 2 we can calculate n(A)n(A-B) = n(A) - n(AnB)18 = n(A) - 25=> n(A) = 18 + 25 = 43now to calculate n(B) we can substitute all the values in equation 170 = 43+ n(B) - 25

• n(AuB) = n(A) + n (B) -n(AnB) —————-1We have n(AnB) = 25 and n(A-B) = 18With these 2 we can calculate n(A)n(A-B) = n(A) - n(AnB)18 = n(A) - 25=> n(A) = 18 + 25 = 43now to calculate n(B) we can substitute all the values in equation 170 = 43+ n(B) - 2570 = n(B) + 18

• n(AuB) = n(A) + n (B) -n(AnB) —————-1We have n(AnB) = 25 and n(A-B) = 18With these 2 we can calculate n(A)n(A-B) = n(A) - n(AnB)18 = n(A) - 25=> n(A) = 18 + 25 = 43now to calculate n(B) we can substitute all the values in equation 170 = 43+ n(B) - 2570 = n(B) + 18n(B) = 70–18 = 52