Final answer:
The question contains typos which make it unclear but seems to refer to constructing a truth table for a logical compound statement. A detailed truth table is provided assuming the correct statement is ((¬p) ∨ g) ∧ (p ∧ (¬g)). The resulting compound statement is never true for the given combinations of p and g.
Step-by-step explanation:
The question seems to contain some typos or irrelevant parts, and therefore isn't entirely clear. However, the request to write a truth table implies that the question is asking about the development of a truth table for a specific logical compound statement. If we are to assume that the student meant to ask for the truth table for the compound statement ((¬p) ∨ g) ∧ (p ∧ (¬g)), we can construct it as follows:
Let's define the two statements involved:
- ¬p (not p)
- p (p itself)
- ¬g (not g)
- g (g itself)
We are looking at the compound statement where (¬p) is OR'd with g, and that result is AND'd with another statement where p is AND'd with (¬g).
The truth table would be:
- p | g | ¬p | ¬g | (¬p ∨ g) | p ∧ (¬g) | ((¬p) ∨ g) ∧ (p ∧ (¬g))
- T | T | F | F | T | F | F
- T | F | F | T | F | T | F
- F | T | T | F | T | F | F
- F | F | T | T | T | F | F
In this table, T represents true, and F represents false. The resulting compound statement is only true when both (¬p ∨ g) and (p ∧ ¬g) are true, which, according to the table, never occurs simultaneously with the given combination of p and g.