Q.In a certain language, 321 means 'Glass of Tea'. 426 means 'Tea is Brown'. 796 means 'Trunks are Brown'. Which of the following represents 'is' in that language?

Quantifiers: From "Some" to "All"

Imagine you're in a classroom. You look around and make observations. "Every student has a notebook." "There is a student who forgot their pencil." These everyday statements are exactly what quantifiers capture in mathematics. They tell us how many objects satisfy a property — and in logic, we care about two extremes: all and at least one.

The Two Core Quantifiers

Universal quantifier ($\forall$) means "for all" or "every." When we write $\forall x$, we're saying: no matter which $x$ you pick from the domain, the statement that follows is true. Think of it as a promise that holds without exception.

Existential quantifier ($\exists$) means "there exists" or "for some." When we write $\exists x$, we're saying: there is at least one $x$ in the domain for which the statement is true. It's a claim of existence — one is enough. …