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Question

If A={a,b,c,d,e}, B={a,c,e,g} and C={b,e,f,g}, verify that:Aāˆ©B-C=Aāˆ©B-Aāˆ©C


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Solution

Prove the given condition

Given,

A={a,b,c,d,e}B={a,c,e,g}C={b,e,f,g}

We have to prove that,

Aāˆ©B-C=Aāˆ©B-Aāˆ©C

For sets P and Q, the notation P-Q denotes the set which has all the elements of P such that the elements are not elements of set Q. It is called their difference.

In general,

P-Q=x:xāˆˆP,xāˆ‰Q

For sets P and Q, the notation Pāˆ©Q denotes the set which has all the elements of P such that the elements are also elements of set Q. It is called their intersection.

In general,

Pāˆ©Q=x:xāˆˆP,xāˆˆQ

So,

LHS=Aāˆ©B-C=a,b,c,d,eāˆ©a,c,e,g-b,e,f,g=a,b,c,d,eāˆ©a,c=a,cRHS=Aāˆ©B-Aāˆ©C=a,b,c,d,eāˆ©a,c,e,g-a,b,c,d,eāˆ©b,e,f,g=a,c,e-b,e=a,e

āˆ“LHS=RHS

Hence proved.


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