Question

Stabititi valoarea de adevar a propozitiilor:
a) 1³+2³+3³∈{n|n∈N,n+1≤16}
b) 8∉{n|n∈N,n=2a,a∈N}

Answer 1

a) 1³+2³+3³∈{n|n∈N,n+1≤16}


1³+2³+3³=1+8+27=36

n+1≤16⇒n≤15 ⇒ n∈{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
36∉{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
este fals


b) 8∉{n|n∈N,n=2a,a∈N}
n∈{0,2,4,6,8,10,12...2n.}

8∈{0,2,4,6,8,10,12...2n.}

este fals