Which of the following expressions denotes a must-be-true condition?

To understand why the expression denoting a must-be-true condition is represented by the conjunction (p ∧ q), it is essential to recognize the nature of logical operators in propositional logic.

In propositional logic, the conjunction operator (∧) signifies that both propositions must be true for the entire expression to be evaluated as true. Specifically, if p represents one condition and q represents another, the expression "p ∧ q" is true only when both p and q are true simultaneously. This implies a strict condition—failure of either p or q leads to the entire conjunction being false. Therefore, when we seek an expression that denotes a must-be-true situation, both conditions being true aligns perfectly with this definition.

In contrast, other expressions serve different purposes; for example, the disjunction (p ∨ q) allows for multiple true scenarios, where either p or q can independently cause the expression to be true. The implication (p → q) states that if p is true, then q must also be true, but does not enforce that both must be simultaneously true. The negation (~p) simply represents that p is not true, which does not specify or require the truth of q.

Thus, the conjunction (p