CS Exam

A = {a, b, c, d}X = {1, 2, 3, 4}Select the definition for f that is a well-defined function.

f = {(a, 2), (b, 3), (c, 3), (d, 1)}

A = {a, b, c, d}X = {1, 2, 3, 4}Each choice defines a function whose domain is A and whose target is X. Select the function that has a well-defined inverse.

f = {(a, 3), (b, 4), (c, 2), (d, 1)}

Select the truth assignment that shows that the argument below is not valid:

p = F q = T

p = T, q = F, and r = F. Select the expression that evaluates to true.

p∨r

Select the converse of p→q

q→p

The propositional variables s and m represent the two propositions: s: It is sunny today. m: I will bring my umbrella. Select the logical expression that represents the statement: "Despite the fact that it is sunny today, I will bring my umbrella."

s∧m

A = {a, b, c, d}X = {1, 2, 3, 4}The function f:A→Xf:A→X is defined as f = {(a, 4), (b, 1), (c, 4), (d, 4)}Select the set corresponding to the range of f.

{1, 4}

A = {1, 2, {3, 4}, {5, 6, 7}}Select the statement that is true.

{1,2}⊆A

A={x∈Z:xis even}A={x∈Z:xis even}B={x∈Z:xis a prime number}B={x∈Z:xis a prime number}D={5,7,8,12,13,15}D={5,7,8,12,13,15}Select the set corresponding to D−(A∪B)D−(A∪B) .

{15}

C={3,5,9,12,15,16}C={3,5,9,12,15,16}D={5,7,8,12,13,15}D={5,7,8,12,13,15}Select the set corresponding to C⊕DC⊕D

{3,7,8,9,13,16}

Select the set that is equal to:3,5,7,9,11,13

{x∈Z:xis odd and3≤x≤14}

A={a,b}A={a,b}B={1,2,3}B={1,2,3}Select the false statement.

|A×B|=5

p = T, q = F, and r = T. Select the expression that evaluates to false.

¬(p∧¬q)

Select the proposition that is a contradiction.

¬(p∨q)∧p

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

∀x(S(x)→A(x))

The domain for variable x is the set of all integers. Select the statement that is true.

∃x(x2<1)

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. Select the statement that is false.

∃x(¬P(x)∧Q(x))

p = F, q = T, and r = T. Select the expression that evaluates to true.

(¬p∧r)∨q

Select the value of ⌈−5.8⌉

-5

f:{0,1}4→{0,1}4f:{0,1}4→{0,1}4f(x) is obtained by removing the second bit from x and placing the bit at the end of the string. For example, f(1011) = 1110. Select the correct value for f−1(0101) .

0110

A = {1, 2, {3, 4}, {5, 6, 7}}Select the correct value for |A|.

4

Select the value of ⌊4.2⌋

4

A={x∈Z:xis even}A={x∈Z:xis even}C={3,5,9,12,15,16}C={3,5,9,12,15,16}Select the true statement.

C−A={3,5,9,15}

Select the law that establishes that the two sets below are equal.A∩(B∪C¯¯¯¯¯¯¯¯¯)=A∩(B¯¯¯∩C¯¯¯)

De Morgan's law

Select the law which shows that the two propositions are logically equivalent. (r∧p)∨¬p∧q)(r∧p)∨¬p∧q) ((r∧p)∨¬p)∧((r∧p)∨q)

Distributive law

f:{0,1}3→{0,1}3f:{0,1}3→{0,1}3f(x) is obtained by removing the second bit from x and placing the bit at the end of the string. For example, f(101) = 110.Select the correct description of the function f.

One-to-one and onto

f:Z→Z.f(x)=⌈x/3⌉Select the correct description of the function f.

Onto but not one-to-one

f:{0,1}4→{0,1}3f:{0,1}4→{0,1}3f(x) is obtained from x by removing the first bit.For example, f(1000) = 000.Select the correct description of the function f.

Onto but not one-to-one

Select the statement that is not a proposition.

Take out the trash.

Select the statement that is false.

Z⊂R+

The propositional variables b, v, and s represent the propositions: b: Alice rode her bike today. v: Alice overslept today. s: It is sunny today. Select the logical expression that represents the statement: "Alice rode her bike today only if it was sunny today and she did not oversleep."

b→(s∧¬v)

The domain of discourse are the students in a class. Define the predicates: S(x): x studied for the testA(x): x received an A on the testSelect the logical expression that is equivalent to: "Someone who did not study for the test received an A on the test."

∃x(¬S(x)∧A(x))

Use the definitions below to select the statement that is true.A={x∈Z:xis even}A={x∈Z:xis even}B={x∈Z:−4<x<17}

∅⊂B