5. (c) (A r1 B) u (A n 0) (d)
"EX. 2.3A
3. (a) AU@=A istrue.
(b) ABzBA isfalse.
counterexample: A = {1,2,3}, B = {2, 3,4}, A B = {1}but B A = {4}
(c)AB=ABisfalse. -
counterexample: U = {1,2,3,4, }, A = {1,3}, B = {3,4}
403 = {3} = {1,2,4} but ZmE: {2,4} m
EX. 1.1A
3. £13m : - draw rows of36, 37, 38, , 147 blocks to make a staircase.
- make a copy of the staircase and turn it 180°.
- t the two staircases together to form a rectangle.
- count the number of blocks in the rectangle.
- divide it by two to nd th
EX. 8.2B
9. Let x be the original number and y be the answer, then
4m + 16 _ 7 _
2 9
Solving the equation for 3:, we get
4m'+16=2(y+7)
4m=2(y+7)16
4m=2y+1416
4x 2 2y 2
: 2(y-l)
4
mzygl
Ans: Thus, to get the original number, take the answer, subtract 1 a
One more thing: We do not really have the slope at "x", but rather the average slope between
"x" and "x+dx". To get around this, we DEFINE the slope at "x" to be the limiting value when "dx"
gets very small. From the above expression, it might look as tho