Question

Let the Universal Set, S, have 52 elements. A and B are subsets of S. Set A contains 26 elements and SetB contains 14 elements. If the total number of elements in either A or B is 27, how many elements are inA but not in B?

Answer 1

Number of elements in A but not in B = 13

Step-by-step explanation

Step 1: Given that:

n(S) = 52

n(A) = 26

n(B) = 14

n(A U B) = 27

Step2: Using the Venn Diagram

Step 3: Determine the value of n(A n B)

n(A U B) = n(A) + n(B) - n(A n B)

27 = 26 + 14 - n(A n B)

n(A n B) = 40 - 27

n(A n B) = 13

Step 4: Determine the number of elements in A but not in B

n(A - B) = n(A) - n(AnB)

n(A - B) = 26 - 13

n(A - B) = 13

Hence, number of elements in A but not in B = 13