.Convert the following integers from decimal notation to binary notation.

4532

1023

2Convert each of the following integers from binary notation to hexadecimal notation.

101010101010

111011101110111

3.

Convert the following hexadecimal numbers to decimal numbers.

DE516

2AB.416

4.

Determine whether the following are propositions. Give the truth value of the propositions.

Asia is the largest of the Earth’s seven continents.

4 + x = 5

2 * 3 = 5

Answer this question

The human heart is shaped like an upside-down pear and is located slightly to the left of center inside the chest cavity

5. Give the inverse, converse and contrapositive for each of the following propositions.

a) If x + y = 1 then x2 + y2 ≥ 1

b) If 2 + 2 = 4 then 3 + 3 = 8

6.Prove or disprove that the two propositions in each pair are equivalent.

a. (p (q r)) , ((p q ) ( p r ))

b. (p (q r)) , (( p q ) ( p r ))

c. (( p q ) r ) , ( p ( q r))

7. Determine whether the following proposition is a tautology.

((¬p ᴠ ¬q) (p ᴧ q ᴧ r)) (pᴧ q)

Transcribed Image Text:10 (18) WhatsApp Assignment b Success Confirmation of Qu X W ITNB2103-Assignment_1- × + Office Editing for Docs, Sheets & Slides | chrome-extension://bpmcpldpdmajfigpchkicefoigmkfalc/views/app.html X Course | HLS2X | edX Assigment Unitar $ 102 - Invoice Home W SQL Tutorial Google Webhelp Other bookmarks ITNB2103_-_Assignment_1-PJJ (2).docx W Download 6 Share File Edit Format Tools Help E Q Q в IU A A - Normal Century Go... 10 8. For the following circuits, find a Boolean expression and construct the truth table. а) A b) A Z В 2 31 3 GB V 23:36 N B.
$10 (18) WhatsApp Assignment b Success Confirmation of Qu X W ITNB2103-Assignment_1- × + Office Editing for Docs, Sheets & Slides | chrome-extension://bpmcpldpdmajfigpchkicefoigmkfalc/views/app.html X Course | HLS2X | edX Assigment Unitar $ 102 - Invoice Home W SQL Tutorial Google Webhelp Other bookmarks ITNB2103_-_Assignment_1-PJJ (2).docx W Download 6 Share File Edit Format Tools Help Q Q в I U A - Normal Century Go... 10 A - Determine whether these functions are onto, one-to-one, both or neither. Justify your answer. a) f(1) = c, f(2) = d, f(3) = a, f(4) = d, f(5) = b b) g(1) = d, g(2) = c, g(3) = a, g(4) = b c) h(1) = b, h(2) = d, h(3) = b, h(4) = c 10. Let A = {c, n, b}, B = {x, y} and C = {0, 1}. Find 9. %3D a) АХВХ С b) СХВХА с) ВХСХ С 11. Let R1 and R2 be the relations on {1,2,3,4} given by R1 = {(1,1), (1,2), (3,4), (4,2)} R2 = {(1,1), (2,1), (3,1), (4,4), (2,2)} List the elements of R, R2 and R2 R1 12. Consider the following relations on {1, 2, 3, 4}. R1 = {(2,2), (2,3),(2,4),(3,2),(3,3),(3,4)} R2 = {(1,1),(1,2),(2,1),(2,2),(3,3),(4,4)} R3 = {2,4),(4,2)} R4 = {(1,2),(2,3),(3,4)} R5 = {(1,1),(2,2),(3,3),(4,4)} a) Which of these relations are reflexive? Justify your answers. b) Which of these relations are symmetric? Justify your answers. c) Which of these relations are antisymmetric? Justify your answer. d) Which of these relations are transitive? Justify your answers. 31 3 GB V 23:37 I!$
Transcribed Image Text:10 (18) WhatsApp Assignment b Success Confirmation of Qu X W ITNB2103-Assignment_1- × + Office Editing for Docs, Sheets & Slides | chrome-extension://bpmcpldpdmajfigpchkicefoigmkfalc/views/app.html X Course | HLS2X | edX Assigment Unitar $ 102 - Invoice Home W SQL Tutorial Google Webhelp Other bookmarks ITNB2103_-_Assignment_1-PJJ (2).docx W Download 6 Share File Edit Format Tools Help Q Q в I U A - Normal Century Go... 10 A - Determine whether these functions are onto, one-to-one, both or neither. Justify your answer. a) f(1) = c, f(2) = d, f(3) = a, f(4) = d, f(5) = b b) g(1) = d, g(2) = c, g(3) = a, g(4) = b c) h(1) = b, h(2) = d, h(3) = b, h(4) = c 10. Let A = {c, n, b}, B = {x, y} and C = {0, 1}. Find 9. %3D a) АХВХ С b) СХВХА с) ВХСХ С 11. Let R1 and R2 be the relations on {1,2,3,4} given by R1 = {(1,1), (1,2), (3,4), (4,2)} R2 = {(1,1), (2,1), (3,1), (4,4), (2,2)} List the elements of R, R2 and R2 R1 12. Consider the following relations on {1, 2, 3, 4}. R1 = {(2,2), (2,3),(2,4),(3,2),(3,3),(3,4)} R2 = {(1,1),(1,2),(2,1),(2,2),(3,3),(4,4)} R3 = {2,4),(4,2)} R4 = {(1,2),(2,3),(3,4)} R5 = {(1,1),(2,2),(3,3),(4,4)} a) Which of these relations are reflexive? Justify your answers. b) Which of these relations are symmetric? Justify your answers. c) Which of these relations are antisymmetric? Justify your answer. d) Which of these relations are transitive? Justify your answers. 31 3 GB V 23:37 I!

Question

4532

1023

2Convert each of the following integers from binary notation to hexadecimal notation.

101010101010

111011101110111

3.

Convert the following hexadecimal numbers to decimal numbers.

DE516

2AB.416

4.

Determine whether the following are propositions. Give the truth value of the propositions.

Asia is the largest of the Earth’s seven continents.

4 + x = 5

2 * 3 = 5

Answer this question

The human heart is shaped like an upside-down pear and is located slightly to the left of center inside the chest cavity

5. Give the inverse, converse and contrapositive for each of the following propositions.

a) If x + y = 1 then x2 + y2 ≥ 1

b) If 2 + 2 = 4 then 3 + 3 = 8

6.Prove or disprove that the two propositions in each pair are equivalent.

a. (p (q r)) , ((p q ) ( p r ))

b. (p (q r)) , (( p q ) ( p r ))

c. (( p q ) r ) , ( p ( q r))

7. Determine whether the following proposition is a tautology.

((¬p ᴠ ¬q) (p ᴧ q ᴧ r)) (pᴧ q)

Accepted Answer

1.
4532   -  10001101101002
1023  - 11111111112
2.
101010101010        -  AAA
111011101110111  -…

.Convert the following integers from decimal notation to binary notation. 4532 1023 2Convert each of the following integers from binary notation to hexadecimal notation. 101010101010 111011101110111 3. Convert the following hexadecimal numbers to decimal numbers. DE516 2AB.416