Question

set a contains 9 letters and 6 numbers. set b contains 8 letters and 3 numbers. 8 letters and 2 numbers are common to both sets a and b. find the number of elements in set a or set b.
the number of elements in set a or set b is □.

Explanation:

Step1: Calculate the number of elements in set A

Set A has \(9\) letters and \(6\) numbers. So, \(n(A)=9 + 6=15\)

Step2: Calculate the number of elements in set B

Set B has \(8\) letters and \(3\) numbers. So, \(n(B)=8 + 3 = 11\)

Step3: Calculate the number of common elements

The common elements (letters and numbers) between A and B: \(n(A\cap B)=8+2 = 10\)

Step4: Use the formula for \(n(A\cup B)\)

The formula is \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\)
Substitute the values: \(n(A\cup B)=15 + 11-10\)
\(n(A\cup B)=16\)

Answer:

\(16\)