Set Theory Practice Solution1





In this page set theory practice solution1 we are going to see solution of practice questions from the worksheet set theory practice questions1.

Question 1

If A ⊂ B,then show that A U B = B (use venn diagram)

Solution:

Since A is the subset of B we have to draw a small circle A inside the large circle B.

A U B = B


Question 2:

If A ⊂ B, then find A ∩ B and A \ B (use venn diagram)

Solution:

Since A is the subset of B we have to draw a small circle A inside the large circle B.

A ∩ B means we have to shade common part of A and B. From this we will get

A ∩ B = A



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}     


Question 4:

If A = {4,6,7,8,9} , B = {2,4,6} and C = {1,2,3,4,5,6},then find

(i) A U (B ∩ C)    (ii) A ∩ (B U C)       (iii) A \ (C \ B)

Solution:

(i) A U (B ∩ C)

(B ∩ C) = {2,4,6} ∩ {1,2,3,4,5,6}

           = {2,4,6}

A U (B ∩ C) = {4,6,7,8,9} U {2,4,6}

                = {2,4,6,7,8,9}

(ii) A ∩ (B U C)

(B U C) = {2,4,6} U {1,2,3,4,5,6}

           = {1,2,3,4,5,6}

A ∩ (B U C) = {4,6,7,8,9} ∩ {1,2,3,4,5,6}

                = {4,6}

(iii) A \ (C \ B)

C \ B = {1,2,3,4,5,6} \ {2,4,6}

        = {1,3,5}

A \ (C \ B) = {4,6,7,8,9} \ {1,3,,5}

               = {4,6,7,8,9}

set theory practice solution1 set theory practice solution1