Math 270A Quiz 1

The domain for variable x is the set of all integers. Select the statement that is true. Select one: a) ∃x(x^2 < 1) b) ∃x(3x = 1) c) ∃x( x^2 < 0) d) ∀x(x^2 = 1)

a) ∃x(x^2 < 1)

The domain for variable x is the set of all integers. Select the statement that is false. Select one: a) ∀x(x^2 >= x) b) ∃x(√x = x) c) ∀x(x^2 ≠ 5) d) ∀x(x^2 > x)

d) ∀x(x^2 > x)

Select the statement that is false. Select one: a. If 4 is a prime number, then 6 is a prime number. b. If 4 is a prime number, then 5 is a prime number. c. If 3 is a prime number, then 5 is a prime number. d. If 3 is a prime number, then 6 is a prime number

d. If 3 is a prime number, then 6 is a prime number

The propositional variables s and m represent the two propositions: s: It is sunny today. m: I will bring my umbrella. Give the logical expression that represents the statement: "Despite the fact that it is sunny today, I will bring my umbrella." Use symbols v, ^, and ~ as needed.

s^m

Select the proposition that is a tautology Select one: A) (p∧q) <-> p B) (p∧q) ->p C) (p∧q)-> ~p D) (pVq) -> p

B) (p∧q) ->p

Use De Morgan's law to write the statement that is equivalent to: "It is not true that the patient has high blood pressure or COVID-19."

b: high blood pressure c: COVID-19 ¬(b∨f)≡¬b∧¬f¬(b∨f)≡¬b∧¬f The patient does not have high blood pressure and the patient does not have COVID-19. (Alternatively, the patient has neither high blood pressure nor COVID-19.)

The propositional variables f, h, and p represent the propositions: f: The student got an A on the final. h: The student turned in all the homework. p: The student is on academic probation Select the logical expression that represents the statement: "The student is not on academic probation and the student got an A on the final or turned in all the homework." a) ~ (p^f) V h b) (~p^f) V h c) ~p^(fVh) d) ~p^f^h

c) ~p^(fVh)

p = F, q = T, and r = T. Select the expression that evaluates to false. Select one a) q ^ r b) qVr c) ~q d) pVr

c) ~q

p = T, q = F, and r = T. Select the expression that evaluates to false. a) (q^r) ->~p b) ~(q^r) ->p c) (q^r) -> p d) (p^r) ->q

d) (p^r) ->q

Write the contrapositive of: "If x≠4, then 3x≠12."

If 3x = 12, then x=4