حل واجبات الجامعة العربية المفتوحة
اتصل : O544321455 - OO966544321455
واتس اب: 966544321455+
ايميل : [email protected]
سكايبي : a_al_shora
حل واجب 0.5.4.4.3.2.1.4.5.5 الجامعة العربية المفتوحة
حل واجبات الجامعة العربية المفتوحة O54.4.3.2.1.4.5.5 - OO96654.4.3.2.1.4.5.5
ايميل : a_al_shora @ h.o.t.m.ail.c.o.m
سكايبي: a_al_shora
واتس اب: OO96654.4.3.2.1.4.5.5
M131: Discrete Mathematics
Q–1: [2+3 Marks]
a) Find a proposition using only and the connective ˅ with the following truth table:
p q ?
F F F
F T T
T F T
T T F
Answer:
b) Using the truth table, determine whether or not the proposition
is a tautology.
Answer:
Q−2: [5×1 marks] Determine whether each of the following is TRUE or FALSE:
a) (1 > 2 or 1 + 2 = 4) if (1 + 1 = 2 and 1 > 2).
b) (124 mod 6 = 4) → (5 | 16).
c) , domain is the set of integers.
d) , domain is the set of integers.
e) .
Answer:
a) b) c) d) e)
Q¬−3: [3+2 marks]
a) Let A = {a, b, c} and B = {1, 2, 3, 4}. Determine whether each of the following is TRUE or FALSE:
i. .
ii. .
iii. .
iv. .
v. .
vi. .
Answer:
i. ii. iii. iv. v. vi.
b) Show that .
Answer:
Q¬−4: [3+2 marks]
a) Consider the decimal number a = 137.
i. Find in set builder notation the set of all positive integers b such that
b ≡ a (mod 5).
ii. Is the number a prime? Explain.
iii. Convert the number a to binary and octal numbers.
Answer:
b) Find the hexadecimal representation of the expansion .
Answer:
Q−5: [2+3 marks]
a) Find the smallest positive integer a in the encryption function
f (x) = (ax + 7) mod 26, 0 ≤ x ≤ 25,
such that the function encodes the letter “H” by “C”.
Answer:
b) Decrypt the message “QHHG KHOS” taking into consideration that you are using the encryption function
f (x) = (x + 3) mod 26, 0 ≤ x ≤ 25.
Answer:
Q¬−6: [2+3 marks] Let R1 = {(x, y): |x - y| ≤ 1} and R2 = {(x, y): 2x + y ≤ 6} be relations on the set A = {1, 2, 3, 4}.
a) List the elements of R1 and R2.
Answer:
b) Find and .
Answer:
Q¬−7: [3+2 marks]
a) Find the transitive closure of R = {(a, a), (b, a), (b, c), (c, a), (c, c), (c, d), (d, a), (d, c)} on the set {a, b, c, d}.
Answer:
b) Find the smallest alence relation on {1, 2, 3} that contains (1, 2) and (2, 3).
Answer:
Q¬−8: [2+3 marks]
a) Let R = {(1, 1), (1, 3), (1, 4), (2, 2), (3, 1), (3, 3), (3, 4), (4, 1), (4, 3), (4, 4), (5, 5), (6, 6)} be an alence relation on A = {1, 2, 3, 4, 5, 6}. Find the alence classes for the partition of A given by R.
Answer:
b) Let R be the partial order relation defined on A = {2, 3, 4, 5, 6, 8, 10, 40}, where xRy means x | y.
i. Draw the Hasse diagram for R.
ii. Find the upper and lower bounds of {4, 8}.
Answer:
حل واجبات الجامعة العربية المفتوحة
اتصل : O544321455 - OO966544321455
واتس اب: 966544321455+
ايميل : [email protected]
سكايبي : a_al_shora
حل واجب 0.5.4.4.3.2.1.4.5.5 الجامعة العربية المفتوحة
حل واجبات الجامعة العربية المفتوحة O54.4.3.2.1.4.5.5 - OO96654.4.3.2.1.4.5.5
ايميل : a_al_shora @ h.o.t.m.ail.c.o.m
سكايبي: a_al_shora
واتس اب: OO96654.4.3.2.1.4.5.5
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