#### Answer

r ↔ (p ᴧ ~q)

#### Work Step by Step

The house is cold if and only if the temperature outside is freezing and the heater isn’t working.
↔ : if and only if
r: the house is cold.
p: the temperature outside is freezing.
ᴧ: and
~q : the heater is not working
The temperature outside is freezing and the heater isn’t working. This will be represented as (p ᴧ ~q)
The house is cold, if and only if the temperature outside is freezing and the heater isn’t working. This will be represented as: r ↔ (p ᴧ ~q)