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Convert the following integers from decimal notation to binary notation.

a) 4532

b) 1023


Can you conclude that A = B if A and B are two sets

with the same power set?


Determine whether each of these pairs of sets are equal.




1. {1,3,3,3,5,5,5,5,5}, {5,3,1}




2. {a,c,t}, {c,a,t}, {t,a,c}




3. {a,c,t}, {a,c,t,o,r}

List the members of the set



I is the set of integers that lies between -1 and 5

Determine whether each of these sets is the power set of a set, where a and b are distinct elements.



1. {0}



2. {0, { a } , { 0, a }}



3. {0, { a } }



4. {0, { a }, { b }, { a, b }}

In a party, there are 12 people with white shirts and 7 people with red shirts;

4 people have black shoes and white shirts;

5 people have black shoes and red shirts;

the total number of people with white or red shirts or black shoes is 21.

How many people have black shoes?


In a party, there are 12 people with white shirts and 7 people with red shirts;

4 people have black shoes and white shirts;

5 people have black shoes and red shirts;

the total number of people with white or red shirts or black shoes is 21.

How many people have black shoes?


Let p and q be propositions


p: 4 is a rational number

q: √3 is an irrational number


Let P(x) denote the statement "x ≥ 10." what are the truth values


  1. P(9)
  2. P(12)
  3. P(-10)
  4. P(10)
  5. P(0)


Let P(x) be the statement "x has develop a program in JAVA", where the domain for x consist of all student. write a statement in English corresponding to the for


  1. ?x P(x)
  2. ?x ~P(x)
  3. ?x P(x)
  4. ~?x P(x)
  5. ~? ?x P(x)


Let P(x) denote the sentence 2x + y = 5. What are the truth values of the following where the domain of x and y is the set of all integers.


  1. ?x ?y P( x,y)
  2. ?x ?y P( x,y)
  3. ?x ?y P( x,y)
  4. ?x ?y P( x,y)

3. Let U={positive integers between 1 and 15 inclusive)


A₁ = (21-1,3-2,4i -3,5-4) for i=1,2,3,... where A, SU for every i


Find


a)


U A₂


1=2


A


A-1


E=k•10+1