If n(A U B)=22, n(A ∩ B)=8, and n(B)=12, find n(A)
If n(A)=8, n(B)=14 and n(A ∩ B)=5, find n(A U B)
n(A U B) = n(A) + n(B) - n(A ∩ B)
22 = n(A) + 12 - 8
n(A) = 18
I figure you can get the other answer
To find n(A) using the given information, we can use the formula:
n(A U B) = n(A) + n(B) - n(A ∩ B)
Given that n(A U B) = 22, n(A ∩ B) = 8, and n(B) = 12, we can substitute the values into the formula:
22 = n(A) + 12 - 8
Rearranging the equation:
22 = n(A) + 4
Subtracting 4 from both sides:
n(A) = 22 - 4
n(A) = 18
Therefore, n(A) = 18.
For the second question, to find n(A U B) using the given information, we can use the formula:
n(A U B) = n(A) + n(B) - n(A ∩ B)
Given that n(A) = 8, n(B) = 14, and n(A ∩ B) = 5, we can substitute the values into the formula:
n(A U B) = 8 + 14 - 5
n(A U B) = 17
Therefore, n(A U B) = 17.
To find n(A) when n(A U B) = 22, n(A ∩ B) = 8, and n(B) = 12, we can use the formula for finding the size of the union of two sets:
n(A U B) = n(A) + n(B) - n(A ∩ B)
Plugging in the values given:
22 = n(A) + 12 - 8
We can solve this equation by isolating n(A):
22 - 12 + 8 = n(A)
Therefore, n(A) = 18.
Similarly, to find n(A U B) when n(A) = 8, n(B) = 14, and n(A ∩ B) = 5, we can rearrange the formula:
n(A U B) = n(A) + n(B) - n(A ∩ B)
Plugging in the values given:
n(A U B) = 8 + 14 - 5
Therefore, n(A U B) = 17.