Question

33 Fie mulţimile: A = {n\n e N, n = 3° +2°, unde a = {1, 2}, b = {0, 1, 2, 3};
B = {m\me N, m = 2-n-5, unde ne A}; C = {plpe N₁ p = 5² + m - 17, unde me B}.
a Scrieți mulțimile prin enumerarea elementelor.
b Calculați An B; AUBUC; B-C.

Answer 1

Explicație pas cu pas:

a)

A = {n | n ∈ N, n = 3° + 2°, unde a = {1, 2}, b = {0, 1, 2, 3}}

a = 1 => n = 3¹+2⁰ = 3+1 = 4; n = 3¹+2¹ = 3+2 = 5; n = 3¹+2² = 3+4 = 7; n = 3¹+2³ = 3+8 = 11

a = 2 => n = 3²+2⁰ = 9+1 = 10; n = 3²+2¹ = 9+2 = 11; n = 3²+2² = 9+4 = 13; n = 3²+2³ = 9+8 = 17

=> A = {4, 5, 7, 10, 11, 13, 17}

B = {m | m ∈ N, m = 2×n-5, unde n ∈ A}

=> B = {3, 5, 9, 15, 17, 21, 29}

C = {p | p ∈ N, p = 5² + m - 17, unde m ∈ B}

p = 25 + m - 17 = m + 8

=> C = {11, 13, 17, 23, 25, 29, 37}

b)

A∩B = {5, 17}

AUBUC = {3, 4, 5, 7, 9, 10, 11, 13, 15, 17, 21, 23, 25, 29, 37}

B-C = {3, 5, 9, 15, 21}