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.

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.
Solution:
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}
             = {a,e} ---- (1)
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}   
            = {a,e} ---- (2)
(1) = (2)

Hence proved