Question

question 1
given ( n(acap b)=17 ), ( n(a)=42 ), ( n(b)=144 ), calculate ( n(acup b)=? ) and enter your answer in the box provided below.

question 2
given ( n(ecup f)=123 ), ( n(e)=90 ), ( n(f)=75 ), calculate ( n(ecap f)=? ) and enter your answer in the box provided below.

Explanation:

Step1: Use the formula for \(n(A\cup B)\)

The formula is \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\).
Substitute \(n(A) = 42\), \(n(B)=144\), \(n(A\cap B)=17\) into the formula:
\(n(A\cup B)=42 + 144-17\)

Step2: Calculate the value

\(42+144 = 186\), then \(186-17=169\)

Step3: Use the formula for \(n(E\cap F)\)

The formula is \(n(E\cap F)=n(E)+n(F)-n(E\cup F)\)
Substitute \(n(E) = 90\), \(n(F)=75\), \(n(E\cup F)=123\) into the formula:
\(n(E\cap F)=90 + 75-123\)

Step4: Calculate the value

\(90+75=165\), then \(165 - 123=42\)

Answer:

169
42