15 terms

Let P be the statement "6 is even" and Q be the statement "1 ∈ {2,3,4}".

Determine the truth value of P ^ Q

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?

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**

P | Q | P⇒Q | (P⇒Q)⇒P

--------------------------

T | T | T |

T | F | F |

F | T | T |

F | F | 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.