WGU D420 Discrete Math 1 Exam 2025/2026 ACTUAL
COMPLETE REAL EXAM QUESTIONS WITH ACCURATE
ANSWERS (VERIFIED ANSWERS) | GET IT RIGHT!! ALREADY
GRADED A+ / 2025 BRAND NEW!!
Two sets are equal if and only if each is a subset of the other: -
ANSWER-A = B
if and only if A ⊆ B and
B⊆A
The process of applying a function to the result of another
function is called -
ANSWER-
composition.
f and g are two functions, where f: X → Y and g: Y → Z. The
composition of g with f, denoted g ο f, is the function (g ο f): X
→ Z,such that for all x X, (g ο f)(x) = g(f(x)). - ANSWER-see pic.
∈
It is possible to compose more than two functions.
Composition is associative, so the order in which one
,composes the functions does not matter: - ANSWER-f ο g ο h =
(f ο g) ο h = f ο (g ο h) = f(g(h(x)))
Logic uses ∧, ∨ and ¬, and Boolean algebra - ANSWER-
uses the familiar
symbols of +, -,
and x¯.
Boolean multiplication, denoted by •, applies to two elements
from {0, 1} and obeys the standard rules for multiplication. The
results of the multiplication operation are the same as the
logical ∧ ("and") operation. - ANSWER-see pic
Boolean addition, denoted by +. Or operation. - ANSWER-see
pic
The complement of an element, denoted with a bar symbol,
reverses that element's value. - ANSWER-Complementing a
Boolean value is analogous to applying the ¬ ("not") operation
in logic.
The exclusive or or XOR operation, denoted by ⊕, is a logical
operation that outputs 1 only when the inputs are different.
Equivalently, p⊕q=p⋅q¯+p¯⋅q. - ANSWER-The results of the
,XOR operation is the same as the result of the logical operation
p⊕q=(p∧¬q)∨(¬p∧q).
see pic
Precedence rules for Boolean operations - ANSWER-• Boolean
multiplication takes precedence over Boolean addition.
• The complement operation is applied as soon as the entire
expression under the bar is evaluated.
• Parentheses can be used to override the precedence rules.
In predicate logic, a special symbol (≡) is used to denote logical
equivalence. -
ANSWER-In Boolean algebra, the equal sign (=) is used to
denote logical
equivalence.
laws for boolean algebra - ANSWER-see pic
A Disjunctive normal form is: - ANSWER-the sum of products of
literals.
A Conjunctive normal form is - ANSWER-the product of sums of
literals.
, literals - ANSWER-Literal = a single Boolean variable or its
complement; for
example, x¯
and x.
For example, the Boolean expression x¯y+xw¯ is in disjunctive
normal form. - ANSWER-The Boolean expression
(x+y+w¯)(x¯+y+w¯) is in conjunctive normal form.
see pic
see examples.
functional completeness - ANSWER-A set of operations is
functionally complete if any Boolean function can be expressed
using only operations from the set. The set {addition,
multiplication, complement} is functionally complete because
any Boolean function can be expressed in disjunctive normal
form which only uses addition, multiplication, and complement
operations.
see pic
COMPLETE REAL EXAM QUESTIONS WITH ACCURATE
ANSWERS (VERIFIED ANSWERS) | GET IT RIGHT!! ALREADY
GRADED A+ / 2025 BRAND NEW!!
Two sets are equal if and only if each is a subset of the other: -
ANSWER-A = B
if and only if A ⊆ B and
B⊆A
The process of applying a function to the result of another
function is called -
ANSWER-
composition.
f and g are two functions, where f: X → Y and g: Y → Z. The
composition of g with f, denoted g ο f, is the function (g ο f): X
→ Z,such that for all x X, (g ο f)(x) = g(f(x)). - ANSWER-see pic.
∈
It is possible to compose more than two functions.
Composition is associative, so the order in which one
,composes the functions does not matter: - ANSWER-f ο g ο h =
(f ο g) ο h = f ο (g ο h) = f(g(h(x)))
Logic uses ∧, ∨ and ¬, and Boolean algebra - ANSWER-
uses the familiar
symbols of +, -,
and x¯.
Boolean multiplication, denoted by •, applies to two elements
from {0, 1} and obeys the standard rules for multiplication. The
results of the multiplication operation are the same as the
logical ∧ ("and") operation. - ANSWER-see pic
Boolean addition, denoted by +. Or operation. - ANSWER-see
pic
The complement of an element, denoted with a bar symbol,
reverses that element's value. - ANSWER-Complementing a
Boolean value is analogous to applying the ¬ ("not") operation
in logic.
The exclusive or or XOR operation, denoted by ⊕, is a logical
operation that outputs 1 only when the inputs are different.
Equivalently, p⊕q=p⋅q¯+p¯⋅q. - ANSWER-The results of the
,XOR operation is the same as the result of the logical operation
p⊕q=(p∧¬q)∨(¬p∧q).
see pic
Precedence rules for Boolean operations - ANSWER-• Boolean
multiplication takes precedence over Boolean addition.
• The complement operation is applied as soon as the entire
expression under the bar is evaluated.
• Parentheses can be used to override the precedence rules.
In predicate logic, a special symbol (≡) is used to denote logical
equivalence. -
ANSWER-In Boolean algebra, the equal sign (=) is used to
denote logical
equivalence.
laws for boolean algebra - ANSWER-see pic
A Disjunctive normal form is: - ANSWER-the sum of products of
literals.
A Conjunctive normal form is - ANSWER-the product of sums of
literals.
, literals - ANSWER-Literal = a single Boolean variable or its
complement; for
example, x¯
and x.
For example, the Boolean expression x¯y+xw¯ is in disjunctive
normal form. - ANSWER-The Boolean expression
(x+y+w¯)(x¯+y+w¯) is in conjunctive normal form.
see pic
see examples.
functional completeness - ANSWER-A set of operations is
functionally complete if any Boolean function can be expressed
using only operations from the set. The set {addition,
multiplication, complement} is functionally complete because
any Boolean function can be expressed in disjunctive normal
form which only uses addition, multiplication, and complement
operations.
see pic
