Question

10) 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: "Everyone who studied for the test received an A on the test." a. $\forall x(A(x)\rightarrow S(x))$ b. $\forall x(S(x) \rightarrow A(x))$ c. $\forall x(S(x) \land A(x))$ d. $\forall x(S(x) \leftrightarrow A(x))$ 11) 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 true. a. $\forall x(Q(x) \rightarrow P(x))$ b. $\forall x(P(x) \rightarrow Q(x))$ c. $\forall x(P(x) \land Q(x))$ d. $\forall x(P(x) \lor Q(x))$

          10) 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:
"Everyone who studied for the test received an A on the test."
a. $\forall x(A(x)\rightarrow S(x))$
b. $\forall x(S(x) \rightarrow A(x))$
c. $\forall x(S(x) \land A(x))$
d. $\forall x(S(x) \leftrightarrow A(x))$
11) 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 true.
a. $\forall x(Q(x) \rightarrow P(x))$
b. $\forall x(P(x) \rightarrow Q(x))$
c. $\forall x(P(x) \land Q(x))$
d. $\forall x(P(x) \lor Q(x))$

10) 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:
"Everyone who studied for the test received an A on the test."
a. ∀ x(A(x)→ S(x))
b. ∀ x(S(x) → A(x))
c. ∀ x(S(x) A(x))
d. ∀ x(S(x) ↔ A(x))
11) 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 true.
a. ∀ x(Q(x) → P(x))
b. ∀ x(P(x) → Q(x))
c. ∀ x(P(x) Q(x))
d. ∀ x(P(x) Q(x))

Added by Joshua M.

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