15 terms

MTH-2215: Applied Discrete Mathematics: Quiz 2

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Let P be the statement "6 is even" and Q be the statement "1 ∈ {2,3,4}".
Determine the truth value of P ^ Q
False
Let P(x) be the open sentence "x^3 = 4," where the domain for x is the set S = {2,3}. What is the truth value of ∃xP(x)?
False
Suppose a variable b has been assigned to the value of 5, and a loop has the form "While (b > 4) Do ... ."
Will we be granted access into this loop?
Yes
The statement ¬P v ¬Q is logically equivalent to the statement ¬(P v Q).
False
Let P(x) be the open sentence "x has three sides," where the domain for x is the set of all triangles. Provide a translation of the statement ∀xP(x).
"Every triangle has three sides."
Let P be the statement "Triangles have five sides and Q be the statement "1 < 2." Determine the truth value of P ⊕ Q
True
Let P(x) be the open sentence "x + 1 < 3" where the domain for x is the set S = {-1,0,1}. What is the truth value of ∀xP(x)?
True
Is "2 >7" a statement?
Yes
Let P be the statement "The set {a,b,c} has exactly 4 elements" and Q be the statement "3 ∈ {1,2,4}". Determine the truth value of the statement P ⇒ Q.
True
Let P be the statement "The sun is made of lemons" and Q be the statement "8 > 1." Express the statement P v Q in words.
"The sun is made of lemons or 8 > 1."
Let P be the statement "The moon is made of cheese" and Q be the statement "19 ∈ {1,2,3,4,5,6,7,8,9,10}". Determine the truth value of P ⇔ Q.
True
Is "3x = 9" a statement?
no
Which (if any) entries in the last column (the ones in boldface) of the table below are incorrect?
P | Q | P⇒Q | (P⇒Q)⇒P
--------------------------
T | T | T | T
T | F | F | T
F | T | T | T
F | F | T | T
The entries in boldface in the last two rows.
Let P be the statement "A square has seven sides" and Q be the statement "A triangle has one side." Write the statement P ⇒ Q in words.
"If a square has seven sides, then a triangle has one side."
Let P be the statement "9 ÷ 0 is undefined". Express the statement ¬P in words and determine its truth value.
"9 ÷ 0 is defined." False.