Question

3. (a) Fill in True if the following equation is correct and False otherwise. 1 · 10^2 + 2 · 10^1 + 3 · 10^0 = 1 · 2^6 + 1 · 2^5 + 1 · 2^4 + 1 · 2^3 + 0 · 2^2 + 1 · 2^1 + 1 · 2^0 ? True ? False (b) In our standard base 10 number system we represent the number given in part (a) as 123. Which of the Left-Hand-Side or Right-Hand-Side of the above equality gives this representation? ? Left-Hand-Side ? Right-Hand-Side (c) In the base 2 (binary) number system we represent the number given in part (a) as 1111011. Which of the Left-Hand-Side or Right-Hand-Side of the above equality gives this representation? ? Left-Hand-Side ? Right-Hand-Side 4. In this problem we learn a method for encoding each of the subsets of the set {a, b, c} with a binary number. Fill in each of the blank cells in the table below. Subsets of {a, b, c} | Binary representation | Base 10 representation ? | 000 | 0 {a} | 100 | 4 | 010 | 2 {c} | | 1 {a, b} | | 6 {b, c} | 011 | 3 | 101 | 5 {a, b, c} | | 7 5. We can think of the table in problem 4 as describing a function. The domain of this function is the set of all subsets of {a, b, c}, otherwise known as the powerset, denoted P({a, b, c}). The range is all of the natural numbers, written in base 10, from 0 to 7. (a) Consider f?¹ : {0, 1, 2, 3, 4, 5, 6, 7} ? P({a, b, c}) as illustrated in the table above. Fill in the circle for the correct answer. ? f?¹ is a function. ? f?¹ is not a function. (b) Consider f : P({a, b, c}) ? {0, 1, 2, 3, 4, 5, 6, 7} as illustrated in the table above. Fill in the circle for the correct answer. ? f is a bijection. ? f is not a bijection.

          3. (a) Fill in True if the following equation is correct and False otherwise.
1 · 10^2 + 2 · 10^1 + 3 · 10^0 = 1 · 2^6 + 1 · 2^5 + 1 · 2^4 + 1 · 2^3 + 0 · 2^2 + 1 · 2^1 + 1 · 2^0
? True
? False
(b) In our standard base 10 number system we represent the number given in part (a) as 123. Which of the Left-Hand-Side or Right-Hand-Side of the above equality gives this representation?
? Left-Hand-Side
? Right-Hand-Side
(c) In the base 2 (binary) number system we represent the number given in part (a) as 1111011. Which of the Left-Hand-Side or Right-Hand-Side of the above equality gives this representation?
? Left-Hand-Side
? Right-Hand-Side
4. In this problem we learn a method for encoding each of the subsets of the set {a, b, c} with a binary number. Fill in each of the blank cells in the table below.
Subsets of {a, b, c} | Binary representation | Base 10 representation
? | 000 | 0
{a} | 100 | 4
| 010 | 2
{c} | | 1
{a, b} | | 6
{b, c} | 011 | 3
| 101 | 5
{a, b, c} | | 7
5. We can think of the table in problem 4 as describing a function. The domain of this function is the set of all subsets of {a, b, c}, otherwise known as the powerset, denoted P({a, b, c}). The range is all of the natural numbers, written in base 10, from 0 to 7.
(a) Consider f?¹ : {0, 1, 2, 3, 4, 5, 6, 7} ? P({a, b, c}) as illustrated in the table above. Fill in the circle for the correct answer.
? f?¹ is a function.
? f?¹ is not a function.
(b) Consider f : P({a, b, c}) ? {0, 1, 2, 3, 4, 5, 6, 7} as illustrated in the table above. Fill in the circle for the correct answer.
? f is a bijection.
? f is not a bijection.

3. (a) Fill in True if the following equation is correct and False otherwise.
1 · 10^2 + 2 · 10^1 + 3 · 10^0 = 1 · 2^6 + 1 · 2^5 + 1 · 2^4 + 1 · 2^3 + 0 · 2^2 + 1 · 2^1 + 1 · 2^0
? True
? False
(b) In our standard base 10 number system we represent the number given in part (a) as 123. Which of the Left-Hand-Side or Right-Hand-Side of the above equality gives this representation?
? Left-Hand-Side
? Right-Hand-Side
(c) In the base 2 (binary) number system we represent the number given in part (a) as 1111011. Which of the Left-Hand-Side or Right-Hand-Side of the above equality gives this representation?
? Left-Hand-Side
? Right-Hand-Side
4. In this problem we learn a method for encoding each of the subsets of the set a, b, c with a binary number. Fill in each of the blank cells in the table below.
Subsets of a, b, c | Binary representation | Base 10 representation
? | 000 | 0
a | 100 | 4
| 010 | 2
c | | 1
a, b | | 6
b, c | 011 | 3
| 101 | 5
a, b, c | | 7
5. We can think of the table in problem 4 as describing a function. The domain of this function is the set of all subsets of a, b, c, otherwise known as the powerset, denoted P(a, b, c). The range is all of the natural numbers, written in base 10, from 0 to 7.
(a) Consider f?¹ : 0, 1, 2, 3, 4, 5, 6, 7 ? P(a, b, c) as illustrated in the table above. Fill in the circle for the correct answer.
? f?¹ is a function.
? f?¹ is not a function.
(b) Consider f : P(a, b, c) ? 0, 1, 2, 3, 4, 5, 6, 7 as illustrated in the table above. Fill in the circle for the correct answer.
? f is a bijection.
? f is not a bijection.

Added by Montserrat R.

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