Răspuns:
Explicație pas cu pas:
1) a) -7/11 ∈ Q = adevarat
b) -7/11 ∈ Z = fals
c) +26/13 ∈ Q₊ = adevarat
d) +26/13 = 2 ∈ N = adevarat
2) A = {-1/6 ; +9/3 ; -25/10 ; +49/7 ; -23/23 ; +102/25}
A ∩ (Q-Z) = ?
-1/6 ∈ Q ; +9/3 = 3 ∈ Q;Z ; -25/10 = -5/2 ∈ Q ;
+49/7 = 7 ∈ Q,Z ; -23/23 = -1 ∈ Q,Z ; +102/25 ∈ Q
A ∩ (Q-Z) = {-1/6 ; -25/10 ; +102/25}
3) a) ¹⁰⁾-11/6 si ³⁾-11/20 <=> -110/60 si -33/60
-110/60 < -33/60 => -11/6 < -11/20
b) -7/23 si 19/23 => -7/23 < 19/23
c) ⁷⁾-5/3 si ³⁾-6/7 <=> -35/21 si -18/21 =>
-35/21 < -18/21 => -5/3 < -6/7
d) -15/4 si 16/5 => -15/4 < 16/5
4) 21,5342 ; 21,5(342) ; 21,53(42) ; 21,534(2)
21,5342 = 21,53420000...
21,5(342) = 21,5342342...
21,53(42) = 21,534242...
21,534(2) = 21,534222...
21,5342 < 21,534(2) < 21,5(342) < 21,53(42)
5) a) IxI = 5/9 => x = 5/9 ;
-x = 5/9 => x = -5/9
b) I⁴⁾x-11/4I = 1/2 <=> I (4x-11)/4I = 1/2 <=>
I 4x-11 I = 4/2 = 2
Pentru x ≥ 11/4 => 4x-11 = 2 => x = 13/4
Pentru x < 11/4 => -4x+11 = 2 => x = 9/4
6) A = {x ∈ Z I -5 ≤ (3x+2)/2 < 5}
-5 ≤ (3x+2)/2 < 5 <=> -10 ≤ 3x+2 < 10 <=>
-12 ≤ 3x < 8 I : 3 => -4 ≤ x < 8/3 =>
A = {-4 ; -3 ; -2 ; -1 ; 0 ; 1 ; 2}
cardA = 7
