Vld = Valid It is possible to solve this problem using truth table. This is a discrete math question. I only know that you can find out is it valid or not by using truth table. i am little confused. need help really bad. (p v q) ((¬q)Vr)\) (p v r) Determine if Vld
Vld = Valid It is possible to solve this problem using truth table. This is a discrete math question. I only know that you can find out is it valid or not by using truth table. i am little confused. need help really bad. (p v q) ((¬q)Vr)\) (p v r) Determine if Vld
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3:49
Vld = Valid
It is possible to solve this problem using truth table.
This is a discrete math question. I only know that you
can find out is it valid or not by using truth table. i am
little confused. need help really bad.
((pv q)
Determine if Vld
Proven
Disproven
![Statement
Property
x= y
means "x is defined to be equal to y."
p V p = p pAp = p
pV q = q Vp p^q = q^p
p v (q v r) = (p v q) V r
p^ (q ^r) = (p ^ q) Ar
p V (q Ar) = (p V q) ^ (p V r)
p^ (q V r) ΦΛq) V φΛ γ)
pV (p ^ q) = p p^ (p V q) = p
pVl= p pAT = p
p V (¬p) = T p ^ (¬p) = 1
pVT =T pAl= 1
Idempotence
x:y
means "x is defined to be equivalent to y."
Commutativity
P = Q
means "P implies Q."
Associativity
means "P if and only if Q."
x ES
means "x is an element in the set S."
Distributivity
ACB
means "A is a subset of B."
Absorptivity
p:A → B
means "fis a function from the domain A to the codomain B."
Identity
$*(x)
means "the inverse function of f."
Complementarity
Dominance
(y • ¢)(x): = »($(x))
(Read "Þ following (or composed with) p.")
¬(¬p) = p
Involution
$>(A) := {$(a)|a e A}
(This is the "image" of A under ø.)
1= (T)느 T= (1)느
¬(p v q) = (¬p) ^ (¬q)
¬(p A q) = (-p) v (¬q)
Exclusivity
$<(B) := {a € A|p(a) € B}
(This is the "pre-image" of B under 4.)
DeMorgan's
Im(4) := {$(a)|a e Src(4)}
(This is the "image" of the function p.
Inference
Name
Inference
Name
Note: Im(4) = $>(Src($))).
(p) Cq)
Adjunction
Simplification
p
(p V q) (Gq)
Disjunctive
Syllogism
p
Addition
pv q
{ }
(the empty set)
p → (¬p)
Reductio Ad
Apagogical
Syllogism
N= {0,1,2,3,4, .}
(natural numbers)
-p
Absurdum
(p → q) (p)
(p → q) (¬a)
Z = {.., -3, –2,-1,0,1,2,3, .. }
(integers)
Modus Ponens
Modus Tollens
3{ (a,b e 2) A (b + 0)}
Q :=
(rational numbers)
(p → q) (q → r)
Hypothetical
Syllogism
Conditionalization
p →r
R:= {x |x is on the number line}
(real numbers)
(p → q) (r → )
(p V r) → (q V s)
(p → q) (p →r)
p → (q Ar).
(p → q) (¬p →r)
Resolvent
Dilemma
Complex Dilemma
qVr
(p → q) (¬p → q)
Exhaustive
Compositional
Syllogism
Syllogism
[a, b] := {x € R |a <x< b}
(Note: if a > b, [a, b] = { }and [a, a] = {a})
Fallacy
Name
Fallacy
Name
a..b = {n E Z ]asns b}
(Note if a > b, a..b = { }and a..a = {a})
(p → q) (q)
Asserting the
Conclusion
(p → q) (Gp)
Denying the
Premise
(p → ¬q) (q → -p)
(qר) p)-)A
(p → q) (p → r)
False
Elimination
Non-Sequitur
-(p A q)
False
Reduction
(p # q) (q ± r)
(p # r)
False Transition](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F004a8e3c-a278-4414-bbaf-77c8d726d7bd%2F1fbf8ffe-4dea-49e7-97f7-db554f452647%2F2kb100o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Statement
Property
x= y
means "x is defined to be equal to y."
p V p = p pAp = p
pV q = q Vp p^q = q^p
p v (q v r) = (p v q) V r
p^ (q ^r) = (p ^ q) Ar
p V (q Ar) = (p V q) ^ (p V r)
p^ (q V r) ΦΛq) V φΛ γ)
pV (p ^ q) = p p^ (p V q) = p
pVl= p pAT = p
p V (¬p) = T p ^ (¬p) = 1
pVT =T pAl= 1
Idempotence
x:y
means "x is defined to be equivalent to y."
Commutativity
P = Q
means "P implies Q."
Associativity
means "P if and only if Q."
x ES
means "x is an element in the set S."
Distributivity
ACB
means "A is a subset of B."
Absorptivity
p:A → B
means "fis a function from the domain A to the codomain B."
Identity
$*(x)
means "the inverse function of f."
Complementarity
Dominance
(y • ¢)(x): = »($(x))
(Read "Þ following (or composed with) p.")
¬(¬p) = p
Involution
$>(A) := {$(a)|a e A}
(This is the "image" of A under ø.)
1= (T)느 T= (1)느
¬(p v q) = (¬p) ^ (¬q)
¬(p A q) = (-p) v (¬q)
Exclusivity
$<(B) := {a € A|p(a) € B}
(This is the "pre-image" of B under 4.)
DeMorgan's
Im(4) := {$(a)|a e Src(4)}
(This is the "image" of the function p.
Inference
Name
Inference
Name
Note: Im(4) = $>(Src($))).
(p) Cq)
Adjunction
Simplification
p
(p V q) (Gq)
Disjunctive
Syllogism
p
Addition
pv q
{ }
(the empty set)
p → (¬p)
Reductio Ad
Apagogical
Syllogism
N= {0,1,2,3,4, .}
(natural numbers)
-p
Absurdum
(p → q) (p)
(p → q) (¬a)
Z = {.., -3, –2,-1,0,1,2,3, .. }
(integers)
Modus Ponens
Modus Tollens
3{ (a,b e 2) A (b + 0)}
Q :=
(rational numbers)
(p → q) (q → r)
Hypothetical
Syllogism
Conditionalization
p →r
R:= {x |x is on the number line}
(real numbers)
(p → q) (r → )
(p V r) → (q V s)
(p → q) (p →r)
p → (q Ar).
(p → q) (¬p →r)
Resolvent
Dilemma
Complex Dilemma
qVr
(p → q) (¬p → q)
Exhaustive
Compositional
Syllogism
Syllogism
[a, b] := {x € R |a <x< b}
(Note: if a > b, [a, b] = { }and [a, a] = {a})
Fallacy
Name
Fallacy
Name
a..b = {n E Z ]asns b}
(Note if a > b, a..b = { }and a..a = {a})
(p → q) (q)
Asserting the
Conclusion
(p → q) (Gp)
Denying the
Premise
(p → ¬q) (q → -p)
(qר) p)-)A
(p → q) (p → r)
False
Elimination
Non-Sequitur
-(p A q)
False
Reduction
(p # q) (q ± r)
(p # r)
False Transition
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