A and B are two sets such that n(A-B)= 14+x , n(B-A)=3x and n(A intersection B)=x and if n(A)=n(B) find - Maths - Sets

Question

A and B are two sets such that n(A-B)= 14+x , n(B-A)=3x and n(A
intersection B)=x and if n(A)=n(B) find x and n(AUB)

Tanveer Sofi · Accepted Answer

We know that for two sets A and B, nA-B=nA-nA∩B    andnB-A=nB-nA∩BNow, it is given that nA-B=14+x ; nB-A=3x   and  nA∩B=xTherefore,nA-B=nA-nA∩B⇒14+x=nA-x⇒nA=14+2x                            
 1Also,nB-A=nB-nA∩B⇒3x=nB-x⇒nB=4x                                    
2Now, it is given thatnA=nB⇒14+2x=4x⇒2x=14⇒x=7
Hence, nA=14+2x=14+27=28             nB=4x=47=28and      nA∩B=x=7Therefore,nA∪B=nA+nB-nA∩B=28+28-7=49

A and B are two sets such that n(A-B)= 14+x , n(B-A)=3x and n(A intersection B)=x and if n(A)=n(B) find x and n(AUB)