King Saud University
Science and Medical Studies Section for girls
College of Science
Department of Mathematics
Name:
Section No.:
Math 151
first Term 1431-32H
first midterm Exam
90 minuets
Student No.:
Sequence No.:
Question No.
Mark
I
II
III
IV
Total
Question I
Choose the correct answers and write them in the following table:
Question
Answer
1
2
3
4
1) The compound proposition 𝒑∧(p→q)→q is
a) a tautology
b) a contradiction
5
6
7
c) a contingency
2) The two compound propositions (𝒑 ∧ 𝒒) → 𝒓 and (𝒑 ∧ −𝒓) → −𝒒 are
a) logical equivalent
b) not logical equivalent
3) The argument
a) valid
 p  q , r q , r  s , p  s  p  q  is
b) invalid
4) The statement (∀𝒏)(𝒏𝟐 > 𝑛) where 𝒏𝝐ℕ is
a) true
b) false
5) The statement (∃𝒙𝝐ℚ)(𝒙𝟐 = 𝟐) is
a) true
b) false
6) A  B  A  B where A, B are subsets of X
a) true
b) false
7) The statement "𝟑 ≠ 𝟒 → 𝟑 + 𝟒 = 𝟕" is
a) true
b) false
8) The statement p  q and its converse are not logically equivalent
a) true
b) false
8
Question II
a) Without using the truth table prove the two compound propositions 𝒑 → (−𝒒 ∧ 𝒓) and −𝒑 ∨
−(𝒓 → 𝒒) are logically equivalent.
-p ν –(r  q) = p-(rq) = p -(-r ν q) = p(r Λ–q)
b) A set of propositions is consistent if there is an assignment of truth values to each of the
variables in the propositions that makes each proposition true. Is the following set of
propositions consistent?{ p  q, p  q, q}
Question III
a) Prove that “𝟑|𝒏𝟑 + 𝒏, for all positive integer 𝒏
b) Define and give an example :
1) A statement
2) A tautology
3) A contradiction
Question IV
a)Write the contrapositive of the following: You sleep late if it is Saturday.
b)
Find
P(abcd), where P denotes the power set.