7/25/2019 010215_2010215_1 Logica FMI 010215_1 Logica FMI 010215_1 Logica FMI 010215_1 Logica FMI Logica 010215_1 L

1/1

LUCRARE SCRISA LA LOGICA

01.02.2015

Numele ................................................................ Grupa ...............

1. Aratati ca propozitia (p qr) ((p q)(p r)) estetautologie folosind:a) tabele de adevarb) tablouri semantice.

2. Demonstrati formal:A B A B.

3. Fie (A,) o multime ordonata.a) Exprimati n limbaj formal: ,,A admite submultimi bine ordonaten raport cu.b) Exprimati n limbaj cotidian:

(T)(T A(x)(xA((t)(tT tx)(U)(UT ((u)(uUux))))))

4. Decideti daca propozitia

(M)(M Z M= (m)(m Z ()(Mm|)))este adevarata sau falsa. Justificare!

5. Consideram o functief :AB si o submultime nevida Ma luiA. Aratati ca f(f1(f(M))) =f(M).

6. Demonstrati ca pentru orice n Nare loc relatia Cn2n< 4

n

n + 1