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Question 11
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Test 1_a (page 2 of 2)
Let Q(w) be the statement “the word w contains the letter e”. Find the true value of each of these statements:
(i)
Q(lemon)
(ii) Q(false)
a. (i): true, (ii): false
b. (i): false, (ii): false
c.
(i): true, (ii): true
d. (i): false, (ii): true
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Question 12
What is the value of x after this statement, assuming the initial value of x is 3?
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‘If x equals to one then x:=x+2 else x:=0’.
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a. 0
b. 3
c.
5
d. 2
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Test 1_a (page 2 of 2)
Question 13
Write the statement in the "If-then" form.
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"It is necessary to score a goal to win the match".
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Which one is true?
(i) If the team scores a goal, they will win the match.
(ii) If the team doesn't score a goal, they don't win the match.
a. Only (ii)
b. Only (i)
c.
Both
d. Neither
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Question 14
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Assume that p, q and r are propositions with truth values F, T and F respectively. Find the truth value of the following
compound proposition.
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a. T or F
b. T
c.
F
d. None of the other choices is correct.
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Test 1_a (page 2 of 2)
Question 15
Suppose that the variable x represents students, F(x) means “x is a freshman”, and M(x) means “x is a math major”.
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into English statement.
a. Every math major is a freshman
b. Some freshmen are math majors
c.
None of these
d. No math major is a freshman
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Question 16
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Let p, q and r be the propositions. p: You get an A on the final exam. q: You do every exercise in this book. r: You get
an A in this class. Write a proposition to express this sentence "Getting an A on the final and doing every exercise in
this book is sufficient for getting an A in this class."
a.
p ∧ p∧t
b. ( p ∧ q ) → r
c.
(p→q)→r
d.
p v p∧t
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Question 17
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Test 1_a (page 2 of 2)
Let p and t be the proposition. p: I bought a lottery ticket this week. t: I won the million dollar jackpot on Monday.
Express the English sentence "Either I did not buy a lottery ticket this week, or else I did buy one and win the million
dollar jackpot" as a proposition.
a. ¬ p v ( p ∧ t )
b.
p ∧ (p∧t)
c.
¬p ∧(pvt)
d. p → ( p v t )
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Question 18
Negation of
" −1 < x ≤ 4 "
is logically equivalent to
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a.
x ≤ −1 or x ≥ 4
b.
x ≤ −1 or x > 4
c.
x ≥ −1 or x > 4
d.
x < −1 or x > 4
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Test 1_a (page 2 of 2)
Question 19
Which of the following statement is a proposition?
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a. None of these.
b. The only odd prime number is 2.
c.
God bless you!
d. What is the time now?
e. Get me a glass of milkshake
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Question 20
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Let us call P = "I am a student in FUHCM", Q = "I have a good job". Thus, P → Q means
a. If I do not have a good job, I am not a student at FUHCM.
b. The sufficient for me to have a good job is that I am a student at FUHCM.
c.

.
If I have a good job, then I am a student at FUHCM.
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