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

Let P = {a, b, c}, Q = {g, h, x, y} and R = {a, e, f, s}. Find the following (i) P \ R (ii) Q ∩ R (iii) R \ (P ∩ Q)

Question 3 :

Let P = {a, b, c}, Q = {g, h, x, y} and R = {a, e, f, s}. Find the following

(i) P \ R (ii)  Q ∩ R    (iii) R \ (P ∩ Q)

Solution :

(i) To find P \ R we have to choose the common elements from both P and R and we have to write remaining elements in P.

P \ R  = {a, b, c} \ {a, e, f, s}

 = {b, c}

(ii) To find Q ∩ R we have to write the common elements in Q and R.

Q ∩ R  = {g,h,x,y} ∩ {a,e,f,s}

there is no common elements in both Q and R

Q ∩ R  = Ø

(iii) R \ (P ∩ Q)

 P ∩ Q = {a,b,c} ∩ {g,h,x,y}

There is no common elements in both P and Q

P ∩ Q = Ø

R \ (P ∩ Q)  = {a,b,c} \ Ø

 = {a,b,c}