Mă ajută cineva va rog frumos
Inregistrati-va pentru a beneficia de cunostintele comunitatii, a pune intrebari sau a a raspunde la intrebarilor celorlalti.
Suntem o comunitate care incurajeaza educatia si in care se intalnesc know-how-ul si experienta cu perspective inovative de abordare a problemelor.
Autentificati-va pentru a pune intrebari, a raspunde la intrebarilor celorlalti sau pentru a va conecta cu prietenii.
V-ati uitat parola ? Introduceti adresa de email si veti primi o noua parola.
Please briefly explain why you feel this question should be reported.
Va rugam explicate, pe scurt, de ce credeti ca aceasta intrebare trebuie raportata.
Motivul pentru care raportezi utilizatorul.
1.a)Adevarat
b), c) nu sunt propozitii
d)Adevarat
e)Fals
2.a)![2\sqrt2+\frac{\sqrt2-4}{\sqrt2}=2\sqrt2+1-\frac{4}{\sqrt2}=2\sqrt2+1-\frac{4\sqrt2}{2}=2\sqrt2+1-2\sqrt2=1\neq\sqrt2+1](http://latex.codecogs.com/gif.latex?2\sqrt2+\frac{\sqrt2-4}{\sqrt2}=2\sqrt2+1-\frac{4}{\sqrt2}=2\sqrt2+1-\frac{4\sqrt2}{2}=2\sqrt2+1-2\sqrt2=1\neq\sqrt2+1)
, deci p(2) este falsa
, deci p(-2) este adevarata
Propozitia este deci falsa
b)p(2):
p(-2):
3.a)![A=\{6\}](http://latex.codecogs.com/gif.latex?A=\{6\})
![B=\{-12, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 12\}](http://latex.codecogs.com/gif.latex?B=\{-12,&space;-6,&space;-4,&space;-3,&space;-2,&space;-1,&space;1,&space;2,&space;3,&space;4,&space;6,&space;12\})
![C=\{-3, -2, -1, 0, 1, 2, 3, 4\}](http://latex.codecogs.com/gif.latex?C=\{-3,&space;-2,&space;-1,&space;0,&space;1,&space;2,&space;3,&space;4\})
![A\bigcap B=\{6\}](http://latex.codecogs.com/gif.latex?A\bigcap&space;B=\{6\})
![A\bigcap C=\emptyset](http://latex.codecogs.com/gif.latex?A\bigcap&space;C=\emptyset)
![(A\bigcup B)\bigcap C=(A\bigcap C)\bigcup (B\bigcap C)=\emptyset \bigcup (B\bigcap C)=B\bigcap C=\{-3, -2, -1, 1, 2, 3, 4\}](http://latex.codecogs.com/gif.latex?(A\bigcup&space;B)\bigcap&space;C=(A\bigcap&space;C)\bigcup&space;(B\bigcap&space;C)=\emptyset&space;\bigcup&space;(B\bigcap&space;C)=B\bigcap&space;C=\{-3,&space;-2,&space;-1,&space;1,&space;2,&space;3,&space;4\})
![A-B=\emptyset](http://latex.codecogs.com/gif.latex?A-B=\emptyset)
![B-C=\{-12, -6, -4, 6, 12\}](http://latex.codecogs.com/gif.latex?B-C=\{-12,&space;-6,&space;-4,&space;6,&space;12\})
b)
4.p(6, 2), p(100, 20) sunt adevarate, celelalte sunt false.
5.a)![p:\exists(x)(x\in N \land 3x+1\geq x)](http://latex.codecogs.com/gif.latex?p:\exists(x)(x\in&space;N&space;\land&space;3x+1\geq&space;x))
![q:\forall(x)(x\in R \implies 3+x-4\neq 0)](http://latex.codecogs.com/gif.latex?q:\forall(x)(x\in&space;R&space;\implies&space;3+x-4\neq&space;0))
b)![\neg p:\neg(\exists(x)(x\in N \land 3x+1\geq x))=\forall(x)(\neg x\in N \lor \neg(3x+1\geq x))=\forall(x)(\neg x\in N \lor (3x+1< x))](http://latex.codecogs.com/gif.latex?\neg&space;p:\neg(\exists(x)(x\in&space;N&space;\land&space;3x+1\geq&space;x))=\forall(x)(\neg&space;x\in&space;N&space;\lor&space;\neg(3x+1\geq&space;x))=\forall(x)(\neg&space;x\in&space;N&space;\lor&space;(3x+1<&space;x)))
![\neg q:\neg(\forall(x)(x\in R \implies 3+x-4\neq 0))=\neg(\forall(x)(\neg(x\in R) \lor 3+x-4\neq 0))=\exists(x)(x \in R \land \neg(3+x-4\neq 0))=\exists(x)(x \in R \land (3+x-4= 0))](http://latex.codecogs.com/gif.latex?\neg&space;q:\neg(\forall(x)(x\in&space;R&space;\implies&space;3+x-4\neq&space;0))=\neg(\forall(x)(\neg(x\in&space;R)&space;\lor&space;3+x-4\neq&space;0))=\exists(x)(x&space;\in&space;R&space;\land&space;\neg(3+x-4\neq&space;0))=\exists(x)(x&space;\in&space;R&space;\land&space;(3+x-4=&space;0)))
c) Prima propozitie este falsa, deoarece p-ul este adevarata(spre ex, inegalitatea este satisfacuta pt x=0).
A 2-a prop este adevarata deoarece x=1 este x-ul pt care egalitaeta este satisfacuta.
Multumesc mult 🥰😊