Cinemugam (Kollywood)

What is BODMAS rule ? The rule or order that we use to simplify expressions in math is called "BODMAS" rule. Very simply way to remember  BODMAS rule!       B -----> Brackets first (Parentheses)       O -----> Of (orders :Powers and radicals)       D -----> Division       M -----> Multiplication       A -----> Addition       S -----> Subtraction Important notes : 1. In a particular simplification, if you have both multiplication and division, do the operations one by one in the order from left to right. 2. Division does not always come before multiplication. We have to do one by one in the order from left to right. 3. In a particular simplification, if you have both addition and subtraction, do the operations one by one in the order from left to right. Examples : 12 ÷ 3 x 5  = 4 x 5 = 20 13 - 5 + 9   = 8 + 9 = 17 In the above simplification, we have both division and multiplication. From left to right, we

EXERCISE 1.1 (1) If A ⊂ B,then show that A U B = B (use venn diagram)    Solution (2) If A ⊂ B, then find A ∩ B and A \ B (use venn diagram)    Solution (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 (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 (5) Given A = {a,x,y,r,s}, B = {1,3,5,7,-10},verify the commutative property of set union.    Solution (6) Verify the commutative property of set intersection for A = {l,m,n,o,2,3,4,7} and B = {2,5,3,-2,m,n,o,p}    Solution (7) For A = {x|x is a prime factor of 42}, B ={x|5 < x ≤ 12, x ∈ N} and C = {1,4,5,6} verify A U (B U C) = (A U B) U C.    Solution (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 (9) For A = {5,10,15,20} B = {6,10,12,18,24} and C ={7,10,12,14,

(11) For A = {-3,-1,0,4,6,8,10} B = {-1,-2,3,4,5,6} and C = {-1,2,3,4,5,7},show that (i) A U (B ∩ C) = (A U B) ∩ (A U C) (ii) A ∩ (B U C) = (A ∩ B) U (A ∩ C) (iii) Verify using Venn diagrams Solution: (i) A U (B ∩ C) = (A U B) ∩ (A U C) L.H.S A U (B ∩ C) (B ∩ C) = {-1,-2,3,4,5,6} ∩ {-1,2,3,4,5,7}        = {-1,3,4,5} A U (B ∩ C) = {-3,-1,0,4,6,8,10} U {-1,3,4,5}             = {-3,-1,0,3,4,5,6,8,10}  --- (1) R.H.S (A U B) ∩ (A U C) (A U B) = {-3,-1,0,4,6,8,10} U {-1,-2,3,4,5,6}         = {-3,-2,-1,0,3,4,5,6,8,10} (A U C) = {-3,-1,0,4,6,8,10} U {-1,2,3,4,5,7}        = {-3,-1,0,2,3,4,5,6,7,8,10} (AUB)∩(AUC)={-3,-2,-1,0,3,4,5,6,8,10} ∩ {-3,-1,0,2,3,4,5,6,7,8,10}              = {-3,-1,0,3,4,5,6,8,10}  --- (2) (1) = (2) A U (B ∩ C) = (A U B) ∩ (A U C) Hence proved (ii) A ∩ (B U C) = (A ∩ B) U (A ∩ C) A = {-3,-1,0,4,6,8,10} B = {-1,-2,3,4,5,6} and C = {-1,2,3,4,5,7} L.H.S (B U C) = {-1,-2,3,4,5,6} U {-1,2,3,4,5,7}