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Please find the answer below each question, some answers might be wrong please
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Question:
Let
m be an integer with m > 1. R on the set of integers is an equivalence
relation if
Select
one:
a.
{(a, b) | a ≡ b (mod m)}
b.
{(a, b) | a ≡ a (mod b)}
c.
{(a, b) | b ≡ b (mod a)}
d.
{(a, b) | b ≡ a (mod m)}
The Correct answer is: {(a, b) | a ≡ b (mod m)}
Question:
Consider
the statement: ∀ x, y E
Z if both xy and x + y are even, then
Select
one:
a.
both x and y are odd
b.
both x and y are even
c.
x is even and y is odd
d.
x is odd and y is even
The Correct answer is: both x and y are even
Question:
If
A = {0, 1}, B = {1, 2}, and C = {0, 1, 2} then what of the following isn’t in A
× B × C ?
Select
one:
a.
(1, 1, 0)
b.
(2, 2, 0)
c.
(1, 1, 1)
d.
(1, 2, 2)
The Correct answer is: (2, 2, 0)
Question:
Let
A, B, and C be sets. Identify the the correct one among the following
Select
one:
a.
None of these
b.
A ∩ (B ∩ C) = (C ∪ B) ∪ A
c.
A ∪
(B ∩ C) = (C ∪ B) ∩ B
d.
A ∩ (B ∪
C) = (C ∩ B) ∩ A
The Correct answer is: None of these
Question:
Let
f1 and f2 be functions from R to R such that f1(x) = x2 and f2(x) = x − x2.
What are
the
functions f1 + f2 and f1 f2?
Select
one:
a.
x2 and x4 – x3
b.
x and x3 – x2
c.
x3 and x2 – x3
d.
x and x3 − x4
The Correct answer is: x and x3 − x4
Question:
Determine
for what of the following for “f” is not a one-to-one function:
Select
one:
a.
f for f (x) = x + 1 from the set of real
numbers to itself
b.
f from {a, b, c, d} to {1, 2, 3, 4, 5}
with f (a) = 4, f (b) = 5, f (c) = 1, and f (d) = 3
c.
f for f (x) = x2 from Z to the set of
integers
d.
f for f (x) = x2 from Z+ to the set of
integers
The Correct answer is: f for f (x) = x2 from Z to the set of integers
Question:
Which
of the following is not a logical equivalence for bi-conditional representation
?
Select
one:
a.
¬(p
→ q) ≡ p ∧¬q
b.
p ↔ q ≡ (p ∧ q) ∨ (¬p ∧¬q)
c.
p ↔ q ≡ ¬p
↔¬q)
d.
All mentioned
The Correct answer is: ¬(p → q) ≡ p ∧¬q
Question:
By
the second law of de-Morgan ¬(r ∨ s) is equivalent to
Select
one:
a.
¬r
∧¬s
b.
¬(¬r ∨¬s)
c.
¬r
∨¬s
d.
¬r
∨
s
The Correct answer is: ¬r ∧¬s
Question:
Let
P(x) be the statement “x + 1 > x.” For the real number domain, qualify the
statement for truth value;
Select
one:
a.
∀x∃P(x)
is true
b.
∀xP(x)
is true
c.
∃x∀P(x)
is true
d.
∃xP(x)
is true
The Correct answer is: ∀xP(x) is true
Question:
For
{Z+: Z+ < 5} verify if ∀xP(x) holds good for P(x) is “x2 < 10”
Select
one:
a.
∀xP(x)
is a conjunction
b.
None of these
c.
∀xP(x)
is false
d.
∀xP(x)
holds good
The Correct answer is: ∀xP(x) is false
Question:
Identify
correct statement/s among the following
Select
one:
a.
The relation"Union of sets" is reflexive,but not symmetric
b.
The relation"parallel of lines" is always an equivalence relation
c.
The relation "Division" is Symmetric
The Correct answer is: The relation"parallel of lines" is always an equivalence relation
Question:
Which
of the following is/are true ?
Select
one or more:
a.
p ∧¬p is always a contradiction
b. ¬p ∨ p is always a tautology
c.
¬p
∨
p is always a contradiction
d.
p ∧¬p is always a tautology
The Correct answer is: ¬p ∨ p is always a tautology, p ∧¬p is always a contradiction
Question:
What
of the following expressions does not imply the negation of the proposition,
“there is an honest politician” if h(x) represents honesty function:
Select
one:
a.
¬∃xH(x)
b.
∃xH(x)
c.
∀x¬H(x)
d.
All of these
The Correct answer is: ∃xH(x)
Question:
“The
sum of two positive integers is always positive” into a logical expression
Select
one:
a.
BOTH :∀x∀y((x
> 0) ∧
(y > 0) → (x +y > 0)) and ∀x∀y(x
+y > 0)
b.
∀x∀y((x
> 0) ∧
(y > 0) → (x +y > 0))
c.
Either ∀x∀y((x
> 0) ∧
(y > 0) → (x +y > 0)) or ∀x∀y(x
+y > 0)
d.
∀x∀y(x
+y > 0)
The Correct answer is: BOTH :∀x∀y((x > 0) ∧ (y > 0) → (x +y > 0)) and ∀x∀y(x +y > 0)
Question:
Which
of the following is/are statement/s
Select
one or more:
a.
How hot the day is
b.
None of these are statements
c.
The temperature is 40 degrees.
d.
It is raining in the summer.
The Correct answer is: The temperature is 40 degrees., It is raining in the summer.
Question:
Let
P be “you can take the flight,”
Let
Q be “you buy a ticket.”
What
of the following notates “you can take the flight if and only if you buy a
ticket”
Select
one:
a.
None of these
b.
Q → P
c.
P → Q
d.
P ↔ Q
The Correct answer is: P ↔ Q