Consider the situations in which a conditional statement, a disjunction, a conjunction, and a negation are true or false.
G
Practice makes perfect
We have been given four statements — a conditional statement, a disjunction, a conjunction, and a negation. We want to find which of them is true when p is true and q is false. Let's first investigate in which situations these statements are true or false.
Conditional Statement: A conditional statement is false when the hypothesis is true and the consequence is false. Otherwise, it is always true.
Disjunction: A disjunction is true when either of its statements is true. Otherwise, it is false.
Conjunction: A conjunction is true when both of its statements are true. Otherwise, it is false.
Negation: A negation is true when the statement is false. Otherwise, it is false.
According to this information, let's create a truth table for the statements.
p
q
F:p → q
G:p ∨ q
H:p ∧ q
I:¬ P
T
T
T
T
T
F
T
F
F
T
F
F
F
T
T
T
F
T
F
F
T
F
F
T
Looking at the table, we can see that the disjunstion is true when p is true and q is false. Therefore, the correct choice is G.
