Predicates & Quantifiers

Let P(x) be the statement "the number x contains the digit 9". Which of these would be true?

• P(x)=25.6
• P(x)=659
• P(x)=81
• P(x)=0

Tags

CCSS.6.EE.B.6

Let P(x) be the statement “on x it snows”, where the domain of x consists of everyday of the year. Express ∀xP(x) in English?

• On some days of the year it snows.
• On every day of the year it snows.
• On every day of the year it does not snow.
• On some days of the year it does not snow.

Let P(x) be the statement “on x it snows”, where the domain of x consists of everyday of the year. Translate "On some days of the year it does not snow."?

• ∃x¬P(x)
• ∃xP(x)
• ∀x¬P(x)
• ∀xP(x)

Let P(x) be the statement "x knows how to yodel" and T(x) be "x is a senior", where the domain is all students. Express ∃xP(x)∧¬T(x) in English?

• Every students knows how to yodel and is a senior.
• For all students, if they are a senior, then they know how to yodel.
• Some students know how to yodel and are not seniors.
• Some students know how to yodel and are seniors.

Tags

CCSS.HSS.CP.A.1

Let P(x) be the statement "x knows how to yodel" and T(x) be "x is a senior", where the domain is all students. Translate "There is only one student who is not able to yodel but is not a senior."?

• ∃x!P(x)∧¬T(x)
• ∀xP(x)∨¬T(x)
• ∃xP(x)∨T(x)
• ∃x!¬P(x)∧T(x)

Let P(x) denote the statement "x-3<12" where the domain consist of all non negative integers. Evaluate the truth value of ∃xP(x) ?

• true
• false

Tags

CCSS.6.EE.B.5

CCSS.6.EE.B.8