CMPT 260 BEGINNER LEVEL QUESTIONS. No direct answers , 2 - 3 steps Explanation wherever its needed.

(a) f k 2 Pjk 1 is a multiple of 7 g (b) f x jx is a fruit and its skin is normally eaten g (c) x 2 Q j1 x 2 Z;x 6 = 0 (d) f 2n jn 2 Z;n < 0g (e) f s js = 1+ 2+ ::: +nfor some n 2Pg (f) 1 n j n 2 f 3;4 ;5 ;6 g (g) f x 2 Z jx = x+ 1g (h) n2 jn = 2; 1;0 ;1 ;2 (i) f n 2 Pjn is a factor of 24 g 2. Describe the following sets using set-builder notation: (a) f5;7 ;9 ; :::; 77;79 g (b) the rational numbers that are strictly between -1 and 1 (c) the even integers (d) f 18; 9;0 ;9 ;18 ;27 ; ::: g (e) f1;1 2 ; 1 3 ; 1 4 ; 1 5 g (f) f1;2 ;3 ;4 ;5 ;6 ;7 g (g) f1;10 ;100 ;1000 ;10000 g 3. Let A = f0, 2, 3 g, B = f2;3 g, and C = f1, 5, 9 g. Determine which of the following statements are true. Give reasons for your answers.

(a) 3 2A (b) f3g 2 A (c) f3g A (d) B A (e) A B (f) /0 C (g) /0 2A (h) A A 4. Let A= f0 ;2 ;3 g;B = f2;3 g;C = f1;5 ;9 g , and let the universal set be U=f0;1 ;2 ; :::; 9g . Determine:

(a) A\ B (b) A[ B (c) B[ A (d) A[ C (e) A B (f) B A (g) Ac (h) Cc (i) A\ C (j) A B 5. Let A= f0 ;2 ;3 g, B = f2 ;3 g , C = f1;4 g, and let the universal set be U=f0;1 ;2 ;3 ;4 g. List the elements of:

(a) A B (b) B A (c) A B C (d) U /0 (e) A Ac (f) B2 (g) B3 (h) B P (B ) 6. How many singleton (one-element) sets are there in P(A ) if jA j= n?

7. Let Aand Bbe nonempty sets. When are A Band B Aequal?

8. Find the binary representation of each of the following positive integers by working through the algo- rithm by hand.

(a) 31 (b) 32 (c) 10 (d) 100 9. What positive integers have the following binary representations?

(a) 10010 (b) 10011 (c) 101010 (d) 10011110000 10. Calculate the following series: (a)å3 i = 1( 2 + 3i) (b) å1 i = 2i2 (c) ån j = 02 j for n= 1;2 ;3 ;4 (d) ån k = 1( 2 k 1) for n= 1;2 ;3 ;4