Question

8. Given P = {a,b,c,d,e},Q = {a,e,i,o,u} and R = {a,c,e,g, }. Verify the associative property of set intersection.

Answer 1

Intersection of two sets :
The intersection of the sets a and b is the set of all the elements which belong to both A and B. It is denoted by A ∩ B (“ A intersection B”).
•if a and b do not have any element in common then A ∩ B= a null set = Ø

SOLUTION :

GIVEN :
P = {a,b,c,d,e} , Q = {a,e,i,o,u}, R = {a,c,e,g}

Intersection of sets is associative :
P ∩ (Q ∩ R) = (P ∩ Q) ∩ R

L.H.S :
P ∩ (Q ∩ R)
(Q ∩ R) = {a,e,i,o,u} ∩ {a,c,e,g}
= {a,e}
P ∩ (Q ∩ R) = {a,b,c,d,e} ∩ {a,e}
P ∩ (Q ∩ R) = {a,e}

R.H.S
(P ∩ Q) ∩ R
(P ∩ Q) = {a,b,c,d,e} ∩ {a,e,i,o,u}
= {a,e}
(P ∩ Q) ∩ R = {a,e} ∩ {a,c,e,g}
(P ∩ Q) ∩ R = {a,e}

L.H.S = R.H.S

Hence proved

HOPE THIS WILL HELP YOU...

Answer 2

Hi ,

It is given that ,

P = { a , b , c , d , e }

Q = { a , e , i , o , u }

R = { a , c , e , g }

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Associative proporty :

P And ( Q and R ) = ( P and Q ) and R

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LHS = P and ( Q and R )

= P and ( { a , e , i , o , u } and { a , c , e , g } )

= P and { a , e }

= { a , b , c , d } and { a , e }

= { a } ----- ( 1 )

RHS = ( P and Q ) and R

= ( { a ,b , c , d , e } and { a , e , i , o , u } ) and R

= { a , e } and R

= { a , e } and { a , c , e g }

= { a , e } -----( 2 )

From ( 1 ) and ( 2 ) ,

LHS = RHS

I hope this helps you.

: )