Propositional Logic

Question

Translate the following statements into symbolic form then determine the truth value : The museum will be open only if it is not a holiday. (O,H -- Assume both statements are true)

Answer 1

~ means "NOT"

The museum will be open only if it is not a holiday.

Translates to ~H --> O.

Assuming (as instructed) that H and O are each true, this conditional statement is true.

The truth table looks like

H O ~H --> O

T T T

T F T

F T T

F F F

You can get this more easily from the statement's equivalent form by (material implication) ~(~H) v O, which is equivalent to (by double negation) H v O.