.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
- .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)
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8.
For the following circuits, find a Boolean expression and construct the truth table.
а)
A
b)
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b Success Confirmation of Qu X
W ITNB2103-Assignment_1- ×
+
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в I U
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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.
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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.
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