Discrete Math I - Fall 02

Exercise 2

Do exercises 3, 5, 7, 9, 11, and 13, on pages 8 and 9 of the textbook and exercises 1,3, and 9 pages 39 and 40.

Let A=(-3,4] and B=(2,9). Find

(1) A^-.

(2) A⁺.

(3) A^*.

(4) 3B.

(5) 3+B.

(6) A - B.

(7) A Ç B.

(8) A È B.

(9) (-3,4]Ç Z.

(10) (-3,4) Ç Z⁺.

Let C=[2,3], and D=[1,4].

(1) Draw [2,3] × [1,4] in the Cartesian plane.

(2) Draw [1,4] × [2,3] in the Cartesian plane.

(3) Draw (2,3) × [1,4] in the Cartesian plane.

(4) Draw [2,3) × (1,4] in the Cartesian plane.

Let A={(x,y) | x²+y² £ 1} (i.e the unit disc), let B={(x,y) | |x| £ 1 and |y| £ 1 }, let C = Z × Z, and let D = Z⁺ × Z⁺.
Find A Ç C, B Ç C, B Ç D, and A Ç D.

Let A={5,-3,2,0,7}, B={3,2,9}. Find A⁺, A^-, A^*, B^-, B⁺, 4A, 6+A, and 6+4A.

Now deifne A Å B to be A Å B = (A- B)È (B- A). Find A Å B for the previous two sets.

Is A Å B = (A È B) - (A Ç B)?

Note: A - B is sometimes denoted A \B.