How is the logical operation "and" symbolically expressed?

The logical operation "and" is symbolically represented by the symbol Λ, also known as "wedge." This symbol is commonly used in propositional logic to indicate that both statements or propositions must be true for the overall expression to be true. For instance, if you have two propositions, P and Q, the expression P Λ Q is true only when both P and Q are true.

This is rooted in the fundamental principles of Boolean algebra, where the "and" operation reflects the conjunction of two conditions. In practical terms, if you consider a real-world scenario such as needing both a valid driver's license and proof of insurance to drive legally, only satisfying both conditions means you can drive. Thus, this logical conjunction is critical for establishing truth values in logical statements.

The other symbols provided represent different logical operations: V indicates "or" (disjunction), -> signifies "implies" (implication), and ~ denotes "not" (negation). Each of these serves a distinct role in logical expressions, but they do not correspond to the conjunction represented by the "and" operation.