Question

Let  . P(x): x²/2 = x

Find the following then identify their truth values.

1. P (1)
2. P (2)
3. ꓯn, P(n)
4. ⱻn, P(n)

Answer 1

$1:\\\frac{1^2}{2}\ne 1\Rightarrow P\left( 1 \right) =0\\2:\\\frac{2^2}{2}=2\Rightarrow P\left( 2 \right) =1\\3:\\P\left( 1 \right) =0\Rightarrow \forall nP\left( n \right) =0\\4:\\P\left( 2 \right) =1\Rightarrow \exists nP\left( n \right) =1$