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Math 225 Final 2.0 Exam Questions And
Answers |Latest 2025 | Guaranteed Pass.
Proposition
A proposition is a declarative sentence that is true or false but not both.
Set
A set is a collection of objects, called members or elements.
Negation
The negation of a proposition p is the proposition that is false when p is true and true when p is
false.
Conjunction
Let p and q be propositions. The conjunction of p and q is the proposition that is true when
both p and q are true and is false otherwise.
Disjunction
Let p and q be propositions. The disjunction of p and q is the proposition that is false when both
p and q are false and is true otherwise.
Symmetric Difference
Let p and q be propositions. The symmetric difference is the proposition that is true when
exactly one of p and q is true and false otherwise.
Conditional Operator (implication)
Let p and q be propositions. Then p implies that q is a new proposition that is only false if p is
true and q is false.
Biconditional
Let p and q be propositions. The biconditional of p and q is the proposition that is true when p
and q have the same truth vale and is false otherwise.
1
, ©FYNDLAY 2024/2025 ALL RIGHTS RESERVED 2:49PM A+
Tautology
A compound if a tautology if it is always true.
Logically Equivalence
The propositions p and q are logically equivalent if the proposition p if and only if q is a
tautology.
Predicate
A predicate P(x) is a statement with a variable x such that when x is given an appropriate value
P(x) becomes a proposition.
Universe of Discourse
The universe of discourse is the set of all values that are appropriate for a given predicate.
AD
Universal quantification
Give a predicate P(x), the universal quantification of P(x) over the set A is the proposition that is
true if P(x) is true for all x in U and is false otherwise.
Existential quantification
Given a predicate P(x), the existential quantification of P(x) over the set U is the proposition
that is true if P(x) is true for all x in U and is false otherwise.
Universal Instantiation
c is an element (arbitrary or particular)
∀x P(x)
∴ P(c)
Universal Generalization
P (c) for an arbitrary c
∴ ∀xP(x)
Existential Instantiation
∃xP(x)
∴ P (c) for some element c
Existential Generalization
P (c) for some element c
∴ ∃xP(x)
2
Math 225 Final 2.0 Exam Questions And
Answers |Latest 2025 | Guaranteed Pass.
Proposition
A proposition is a declarative sentence that is true or false but not both.
Set
A set is a collection of objects, called members or elements.
Negation
The negation of a proposition p is the proposition that is false when p is true and true when p is
false.
Conjunction
Let p and q be propositions. The conjunction of p and q is the proposition that is true when
both p and q are true and is false otherwise.
Disjunction
Let p and q be propositions. The disjunction of p and q is the proposition that is false when both
p and q are false and is true otherwise.
Symmetric Difference
Let p and q be propositions. The symmetric difference is the proposition that is true when
exactly one of p and q is true and false otherwise.
Conditional Operator (implication)
Let p and q be propositions. Then p implies that q is a new proposition that is only false if p is
true and q is false.
Biconditional
Let p and q be propositions. The biconditional of p and q is the proposition that is true when p
and q have the same truth vale and is false otherwise.
1
, ©FYNDLAY 2024/2025 ALL RIGHTS RESERVED 2:49PM A+
Tautology
A compound if a tautology if it is always true.
Logically Equivalence
The propositions p and q are logically equivalent if the proposition p if and only if q is a
tautology.
Predicate
A predicate P(x) is a statement with a variable x such that when x is given an appropriate value
P(x) becomes a proposition.
Universe of Discourse
The universe of discourse is the set of all values that are appropriate for a given predicate.
AD
Universal quantification
Give a predicate P(x), the universal quantification of P(x) over the set A is the proposition that is
true if P(x) is true for all x in U and is false otherwise.
Existential quantification
Given a predicate P(x), the existential quantification of P(x) over the set U is the proposition
that is true if P(x) is true for all x in U and is false otherwise.
Universal Instantiation
c is an element (arbitrary or particular)
∀x P(x)
∴ P(c)
Universal Generalization
P (c) for an arbitrary c
∴ ∀xP(x)
Existential Instantiation
∃xP(x)
∴ P (c) for some element c
Existential Generalization
P (c) for some element c
∴ ∃xP(x)
2
