Discrete Mathematical Methods of Computing Topic: Fundamentals 1. Let A = { x |

Question

Discrete Mathematical Methods of Computing

Topic: Fundamentals

1.

Let A = {x | x is a real number and x < 6}. Identify each of the following as true or false.

(a)3 A

(b)6 A

(c)5 A

(d)8 A

(e)8 A

(f)3. 4 A

2.

Let A = {1, 2, 3, 4, 5}. Which of the following sets are equal to A?

(a){4, 1, 2, 3, 5}

(b){2, 3, 4}

(c){1, 2, 3, 4, 5, 6}

(d){x | x is an integer and x2 25}

(e){x | x is a positive integer and x 5}

(f){x | x is a positive rational number and x 5}

3.

Let A = {x | x is an integer and x2 < 16}. Identify each of the following as true or false.

(a){0, 1, 2, 3} A

(b){3, 2, 1} A

(c){ } A

(d){x | x is an integer and | x| < 4} A

(e)A {3, 2, 1, 0, 1, 2, 3}

4.

Compute

(a)¯ ¯ ¯A ¯ ¯ ¯B

(b)¯ ¯ ¯B ¯ ¯ ¯C

(c)¯ ¯¯¯¯¯¯¯¯ ¯A A

(d)¯ ¯¯¯¯¯¯¯¯ ¯C C

(e)A B

(f)B C

5. A survey of 500 television watchers produced the following information: 285 watch football games, 195 watch hockey games, 115 watch basketball games, 45 watch football and basketball games, 70 watch football and hockey games, 50 watch hockey and basketball games, and 50 do not watch any of the three kinds of games.

write out the first four terms (begin with n = 1) of the sequence whose general term is given.

6. bn = 3n2 + 2n 6

7. d1 = 3, dn = 2dn 1 + 1

find the greatest common divisor d of the integers a and b, and write d as sa + tb.

8. a = 34, b = 58

9. find the least common multiple of the integers.

175, 245

Explanation / Answer

Below are the real number less than 6
<--+---+--+---+---+---+---+---+---+--+--+--+----+--+->
     -8 -7 -6 -5 -4 -3 -2 -1   0   1   2   3   4   5

(a)3 A is true as 3 belong to real number set A.

(b)6 A is false as 6 does not belong to real number set A.

(c)5 A is false as 5 belong to real number set A.

(d)8 A is true as 8 does not belong to real number set A.

(e)8 A is true as -8 belong to real number set A

(f)3. 4 A is true as 3.4 belong to real number set A

2.

Let A = {1, 2, 3, 4, 5}. Which of the following sets are equal to A?

(a){4, 1, 2, 3, 5} and (e){x | x is a positive integer and x 5}

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