Question

Se considera multimile A={xe|N*|x-2<3}. B={xe|N*|7<2x+3<15}. Determinați multimile A, B Aratati ca (AUB) - (AnB) =(A-B) U(A-B).

Answer 1

Explicație pas cu pas:

x - 2 < 3 => x < 5

=> A = {1; 2; 3; 4}

7 < 2x+3 < 15

4 < 2x < 12

2 < x < 6

=> B = {3; 4; 5}

AUB = {1; 2; 3; 4; 5}

A∩B = {3; 4}

(AUB) - (A∩B) = {1; 2; 3; 4; 5} - {3; 4} = {1; 2}

A-B = {1; 2}

(A-B) U (A-B) = {1; 2} U {1; 2} = {1; 2}

=>

(AUB) - (A∩B) = (A-B) U (A-B)

q.e.d.