Math 270A Quiz 2

Select the argument that is invalid. Select one: A) p q ∴ p<-> q B) p -> q pVq --------- ∴p c) pVq ~q --------- ∴ p^~q D) p<->q pVq -------- ∴p

B) p -> q pVq --------- ∴p

The domain for x and y is the set of real numbers. Select the statement that is false. Select one: A) ∀x∃y(x+y >= 0) B) ∃x∀y(x+y >= 0) C) ∀x∃y(xy >= 0) D) ∃x∀y(xy >= 0)

B) ∃x∀y(x+y >= 0)

The domain of discourse are the students in a class. Define the predicates: S(x): x studied for the test A(x): x received an A on the test Select the logical expression that is equivalent to: "Someone who did not study for the test received an A on the test." A) ∃x(~S(x) <-> A(x)) B) ∃x(~S(x) -> A(x)) C) ∃x(~S(x) ^ A(x)) D) ∃x(A(x) -> ~S(x))

C) ∃x(~S(x) ^ A(x))

Select the truth assignment that shows that the argument below is not valid: pVq ~q ---------- ∴ p<->q Select one: a) p = F, q = F b) p=T, q = T c) p = F, q = T d) p = T, q = F

d) p = T, q = F

The domain for variable x is the set {Ann, Ben, Cam, Dave}. The table below gives the values of predicates P and Q for every element in the domain. Name | P(x) | Q(x) --------------------- Ann | F | F --------------------- Ben | T | F --------------------- Cam | T | T --------------------- Dave | T | T --------------------- Select the statement that is false a) ∃x(P(x) -> Q(x)) b) ∃x(P(x) ^ ~Q(x)) c) ∃x(P(x) ^ Q(x)) d) ∃x(~P(x) ^ Q(x))

d) ∃x(~P(x) ^ Q(x))

The domain for variables x and y is the set {1, 2, 3}. The table below gives the values of P(x, y) for every pair of elements from the domain. For example, P(2, 3) = F because the value in row 2, column 3, is F. P| 1 | 2 | 3 ------------ 1 | T | T | T ------------- 2 | T | F | F ------------- 3 | F | T | F ------------- Select the statement that is false: a) ∀x∃yP(x,y) b) ∀y∃xP(x,y) c) ∃x∀yP(x,y) d) ∃y∀xP(x,y)

d) ∃y∀xP(x,y)

Use De Morgan's law to write a statement (in English) that is logically equivalent to: "It is not true that every student got an A on the test."

it is true that there is a student who did not get an A o the test

The domain of discourse are the students in a class. Define the predicates: S(x): x studied for the test A(x): x received an A on the test Write the logical expression that represents: "Everyone who studied for the test received an A on the test."

∀x(S(x) ->A(x))