Q.If $A = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$, determine the truth value of the statement: $\forall\, x \in A,\ x + 5 < 12$.

Some statements assert a condition about every member of a collection, or about at least one member, rather than being a single fixed proposition; the words that express this are called quantifiers. 'For all' / 'for every' is the universal quantifier, written ∀; 'there exists' / 'for some' / 'there is at least one' is the existential quantifier, written ∃. A statement of the form '∀x ∈ A, condition on x' is TRUE only if every single object in the collection A satisfies the condition, and FALSE if even one object in A fails it. A statement of the form '∃x ∈ A such that condition …