in exercises 35-40 write the statement in symbolic form let p: The tent is pitched q: The bonfire is burning
# 38 The bonfire is not burning if and only if the tent is not pitched
We don't seem to have any symbolic logic experts to help you. Sorry. Thanks for trying jiskha
Using "~" for "not"
~q <-> ~p
Note that logically this is the same as
p <-> q
the mathforum site has some good articles on symbolic logic
To write the statement "The bonfire is not burning if and only if the tent is not pitched" in symbolic form, we first need to understand the logical connectives used.
The "if and only if" (iff) connective is represented by the symbol "↔", which represents a biconditional statement. It means that both statements are either true or both are false.
Next, we need to translate the given statements "The bonfire is not burning" and "The tent is not pitched" into symbolic form using propositions. Let's assign the propositions:
p: The tent is pitched
q: The bonfire is burning
Now, we can write the given statement in symbolic form:
"The bonfire is not burning if and only if the tent is not pitched" can be translated to:
q ↔ ¬p
In this symbolic representation, "¬" represents negation or "not". So, ¬p means "not p" or "the tent is not pitched". Therefore, q ↔ ¬p can be read as "q if and only if ¬p" or "The bonfire is not burning if and only if the tent is not pitched".
This is the symbolic form for statement #38.