p∧q (conjunction of p and q)
In logic, the conjunction of two statements p and q, denoted as p ∧ q, represents the statement that is true only when both p and q are true
In logic, the conjunction of two statements p and q, denoted as p ∧ q, represents the statement that is true only when both p and q are true. It is also known as the logical “and” operation.
Here’s a truth table that shows all possible combinations of truth values for p and q, along with the resulting truth value for the conjunction p ∧ q:
| p | q | p ∧ q |
|:—–:|:—–:|:——:|
| False | False | False |
| False | True | False |
| True | False | False |
| True | True | True |
As you can see, the conjunction p ∧ q is true only when both p and q are true. In any other case, it will evaluate to false.
It is important to note that the conjunction operation is commutative, meaning that p ∧ q is logically equivalent to q ∧ p. It is also associative, implying that (p ∧ q) ∧ r is equivalent to p ∧ (q ∧ r).
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