Salahaddin University-Erbil Semester I Discrete Mathematics
College of Science Final Examination February 2020
Lecturer: Dr.Wuria Xoshnaw
Mathematics Department Second Trial Time allowed:120 minutes
Q.1. (12 points)
Define and give an example of each of the following terminologies:
1. Contradiction statement.
2. Empty set.
3. Convergent series.
Q.2. (18 points)
(a) (12 points)
Check whether the following sequences converge or diverge:
1. h-1i
2. h(3)−ni
3. h1
2ni
4. h(−1)ni
(b) (6 points)
State whether the following statements true or false (Explain your answer)
1.
∀a∈Z,∃b∈Rsuch that, −ab2=b+ 1.
2.
∃x∈Q,such that ∀y∈R− {0}, x(x−y−1) = √x
y
Q.3. (15 points)
(a) (6 points)
Let A,Band Cbe arbitrary sets. Prove that
A⊆B∧B⊆C→A⊆C.
(b) (9 points)
Prove that the following statements are equivalent:
(i)
3x+ 2 ∈Ze.
(ii)
x+ 5 ∈Zo.
(iii)
x2∈Ze.
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