The truth table for the given compound statement is:
p q (p∧q) ∼(p∧q) (p∧q)∨∼(p∧q)
T T T F T
T F F T T
F T F T T
F F F T T
How to construct a Truth Table?
To construct the truth table for the compound statement (p∧q)∨[∼(p∧q)], we need to consider all possible combinations of truth values for p and q, and then evaluate the compound statement for each combination. The compound statement contains the logical connectives ∧ (and), ∨ (or), and ∼ (not).
The truth table for the given compound statement is:
p q (p∧q) ∼(p∧q) (p∧q)∨∼(p∧q)
T T T F T
T F F T T
F T F T T
F F F T T
In the truth table, T represents True and F represents False. The column (p ∧ q) represents the conjunction of p and q, and ∼ (p ∧ q) represents the negation of (p∧q). The column (p∧q)∨∼(p∧q) represents the disjunction of (p∧q) and ∼(p∧q). As we can see, the compound statement is always True, regardless of the truth values of p and q.
This truth table was constructed by considering all possible combinations of truth values for p and q, and then evaluating the compound statement for each combination