If P and Q are two sets such that P has 40 elements, P∪Q has 60 elements and P∩Q has 10 elements, how many elements does Q have?

Find Number of Elements in Q

Question:

If \( P \) and \( Q \) are two sets such that

\[ n(P)=40,\quad n(P\cup Q)=60,\quad n(P\cap Q)=10 \]

how many elements does \( Q \) have?

Solution

\[ n(P\cup Q)=n(P)+n(Q)-n(P\cap Q) \] \[ 60=40+n(Q)-10 \] \[ 60=30+n(Q) \] \[ n(Q)=60-30 \] \[ n(Q)=30 \]

Hence,

\[ \boxed{n(Q)=30} \]

Spread the love