Q.If $A = \{3, 5, 7, 9, 11, 12\}$, determine the truth value of: $\forall x \in A$, $x^2 + x$ is an even number

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 on x' is TRUE if at least one object in A satisfies the condition, and FALSE only if NO object in A satisfies it. Checking a quantified statement's truth value therefore means testing the condition, in principle, against every element of the given set.