Examine whether the following statements are true or false:

$\left\{a\right\}\subset \left\{\{a\},\, b \right\}$

{a} ⊂ {{a}, b}

This statement is false.

The set {a} contains only one element, which is 'a'. The set {{a}, b} contains two elements: one is the set {a}, and the other is the element 'b'. Since 'a' is an element of the set {a}, but not of the set {{a}, b}, the statement {a} ⊂ {{a}, b} is false.